For more information, please see full course syllabus of High School Physics

For more information, please see full course syllabus of High School Physics

### Sound

- Sound waves are transmitted as a series of longitudinal pressure differentials.
- Depending on the medium and its specific conditions, the speed of sound can vary greatly.
- "High" pitches correlate to high frequency sound waves, "low" pitches correlate to low frequency sound waves.
- The
*intensity*("loudness") of a sound is determined by the power (P) of the source and the area (A) it is spread over:I = P A. - If the source of the sound spreads perfectly evenly in all direction (which turns out to be difficult in the real world), we can model it with a sphere. The surface area of a sphere is A=4πr
^{2}, which we can use with the above equation. - The human ear can hear a huge variety of intensities. We manage this issue by introducing a logarithmic scale for measuring intensity: the
*decibel*(dB). - If you feel uncomfortable with logarithms, you might want to do a quick review of how they work. Check out the pre-calculus math section on Educator.com to get refreshed with logs.
- We define the idea of
*sound level*(β) using decibels:β = (10 dB) ·log _{10}I I_{0}. - Since waves can interfere with one another, if they have different frequencies, the waves will come in an out of phase with each other. This is the
*beat frequency*:f _{beat}= |f_{1}− f_{2}|. - For objects traveling faster than the speed of sound, we can describe its speed with a
*Mach number*: [v/(v_{s})]. Mach 1 is the speed of sound, Mach 2 is twice the speed of sound, etc.

### Sound

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Speed of Sound 1:26
- Speed of Sound
- Pitch 2:44
- High Pitch & Low Pitch
- Normal Hearing
- Infrasonic and Ultrasonic
- Intensity 4:54
- Intensity: I = P/A
- Intensity of Sound as an Outwardly Radiating Sphere
- Decibels 9:09
- Human Threshold for Hearing
- Decibel (dB)
- Sound Level β
- Loudness Examples 13:44
- Loudness Examples
- Beats 15:41
- Beats & Frequency
- Audio Examples of Beats
- Sonic Boom 20:21
- Sonic Boom
- Example 1: Firework 23:14
- Example 2: Intensity and Decibels 24:48
- Example 3: Decibels 28:24
- Example 4: Frequency of a Violin 34:48

### High School Physics Online Course

### Transcription: Sound

*Hello and welcome back to educator.com. Today weâ€™re going to be talking about sound.*0000

*Sound is one of the waves you encounter the most often in life.*0005

*Such as right now unless youâ€™ve got me on mute, but probably you donâ€™t.*0007

*So sound waves are longitudinal pressure differentials.*0013

*If you had just a normal column of air, all of the air molecules would be equally spaced.*0017

*If you were to push on it suddenly, youâ€™d get this effect where youâ€™d have a bunch of them get bunched up.*0025

*Then that bunching would translate into them being really far spaced out and then theyâ€™d get bunched up again and then theyâ€™d be far spaced out, and then bunched up again and far spaced out.*0030

*That bunching and spacing is the equivalent of a wave going up and down.*0040

*Suddenly weâ€™re seeing the pressure deferential either positive pressure deferential or negative pressure deferential.*0046

*Thatâ€™s how the wave information is being transmitted. Thatâ€™s how energy is being transmitted.*0052

*Is through these compressions and rarefactions moving through it, the compression being where itâ€™s bunched and rarefaction being where there is very few air molecules at that moment.*0056

*Weâ€™re able to have longitudinal pressure differentials and thatâ€™s whatâ€™s happening as Iâ€™m speaking right now.*0065

*My vocal folds, my vocal cords are vibrating the air and those vibrations are being transmitted to the mike*0070

*Which is then being moved, turned into data, which is then transmitted to your speaker, and then the speakers vibrate that same amount of vibration so that you hear my voice reproduced.*0076

*The speed of sound varies greatly from medium to medium, even within the same types of mediums; the speed of sound can vary based on other factors.*0088

*Hereâ€™s some example mediums, so when see air at 0 degrees centigrade and one atmosphere of pressure, the speed of sound is 331 meters per second.*0095

*On a hot day like 30 degrees centigrade suddenly itâ€™s moved up 349 meters per second.*0104

*This is because now the air has more energy in it, it moves faster so itâ€™s going to bounce around so those pressure differentials are going to get moved faster.*0110

*Water at 0 degrees centigrade, one atmosphere is 1482 meters per second, whoops that shouldnâ€™t be 0 degrees centigrade, that should be 20 degrees centigrade right there.*0117

*Water at 20 degrees centigrade, once again more energy, it moves around faster so itâ€™s 1482 meters per second.*0128

*We increase the density by adding salt, turning it into sea water. We get an even higher one, 1520 meters per second.*0134

*Steel. Very uncompressible, so those pressure differentials get moved very quickly as its very hard for it to move.*0140

*That stiffness causes the information, the energy to be transmitted very quickly from one location to the next location along our steel column, bar, what have you.*0146

*So we have a much faster speed of sound. Depending on the material, depending on what weâ€™re dealing with, speed of sound is going to change.*0157

*Thatâ€™s something to keep in mind while weâ€™re working with this.*0163

*Pitch. The human ear is capable of hearing a huge array of frequencies.*0166

*Weâ€™re able to hear the buzzing of a TV set, that sort of background hum of electronics.*0171

*Weâ€™re also able to hear the low base note of a kick drum.*0178

*That huge variety of frequencies that weâ€™re able to hear is what we consider pitch.*0183

*A high pitch sound is one that is a large high frequency, like a violin or a piccolo or the right end of a piano.*0189

*A low pitch on the other hand is one that has a small frequency, like a double bass, a tuba, or the left end of a piano.*0196

*High frequency gives us that high sound like â€˜Ah.â€™ Thatâ€™s a higher frequency than when I talk like this in a low frequency voiceâ€™.*0204

*We experience thisâ€¦experientially, we experience it qualitatively, as a feeling but it is also connected to a qualitative change in the way the thing is measured.*0211

*A young person with good hearing can normally hear sounds anywhere between 20 hertz and 20,000 hertz.*0226

*This is a really wide range of possible frequencies we can pick up.*0232

*As we get older, we start to lose some of that range, especially the higher end.*0236

*Certain diseases and injuries can also damage your ability to hear.*0239

*Pitches below human hearing a called infrasonic and pitches above human hearing are called ultrasonic.*0243

*Infra being Latin for below. Ultra being beyond and sonic being sound.*0250

*Certain animals can actually hear sounds that we canâ€™t hear.*0255

*A dog whistle puts out a frequency that above human hearing in the ultrasonic range.*0258

*The dogâ€™s ears are better calibrated to be able to hear those higher sound notes and so theyâ€™re able to pick it up.*0263

*Bats use ultrasonic sound to be able to locate their prey, locate the area around them, to be able to see, quote unquote â€˜seeâ€™ the area around them.*0268

*Ultrasonic things have certain uses and so theyâ€™re able to send out an ultrasonic chirp and hear it back.*0278

*The way they hear it back, theyâ€™re able to pick up knowledge about the area around them.*0286

*Weâ€™re not able to hear those chirps because theyâ€™re ultrasonic, theyâ€™re above our hearing.*0289

*Intensity. Clearly the frequency or frequencies that we hear is part of the experience of sound but thatâ€™s only part of it.*0296

*The other part is how loud it is, the intensity of the sound.*0302

*A really loud sound is experienced differently than a really quiet sound.*0306

*That dynamic change is part of our experience of sound.*0310

*This is actually a qualitatively measure as well. It is how much power is being put out.*0314

*Remember waves are the transfer of energy through a medium.*0320

*An emitter must be putting out some constant supply of energy or a varying supply of energy but it makes it a little bit easier to talk about as if itâ€™s constant first.*0323

*It has some power output, p, right?*0330

*If our emitter is putting out energy, putting out information to the world around it, itâ€™s putting it out by putting out power.*0333

*Of course, if weâ€™re far from an emitter, the power is more spread out and thus less loud.*0340

*If we walk really far away from an emitter itâ€™s going to seem quieter to us. Thatâ€™s because its power may remain constant but our experience of that power is now spread out over a wider distance.*0344

*It has to travel farther and so the sound waves might start off like this and they spread out a little bit but if weâ€™re over here, theyâ€™re going to spread out and theyâ€™re going to be way wider out.*0356

*Weâ€™re going to get less information for the same area, so weâ€™re going to have the intensity of the sound is going to be determined by how much area the power has to spread over.*0366

*A high intensity is either going to be a small area or a very large power.*0378

*As we either make the power smaller or the area wider weâ€™re going to experience less loudness, less intensity in the sound.*0385

*What area does our power spread over? This is actually a really difficult question because sound often behaves in very complex ways in real life.*0394

*For example if I was sitting in the shower, probably standing, but whatever.*0402

*If I was standing in a shower, say itâ€™s just a square around me.*0407

*My ear is over here and I shoot out sound waves.*0413

*It is not just the sounds waves that manage to shoot backwards towards my ear and get picked up.*0417

*Some of these sounds waves are going to bounce off the container and bounce back to my ear.*0422

*Theyâ€™re going to get spread out and some of the energy will wind up being absorbed by the container, but some of itâ€™s going to get bounced back towards me.*0427

*This is actually, can be a really complicated question, thatâ€™s why your voice can sound and have such different dynamics depending on the room youâ€™re in.*0434

*If youâ€™re in a very large cathedral chamber and youâ€™ve got all this wood around you, youâ€™ve got this big echoey open space.*0440

*The wood picks it up, changes the vibrations slightly. If on the other hand youâ€™re in a tiny, tiled bathroom, youâ€™re going to get a different sound.*0447

*Once again, those very hard tiles vibrate; reflect almost all the energy, almost all that information.*0455

*Itâ€™s a small space so it all bounces back and gets picked up by your ear again.*0462

*Different spaces, different perception of the sound because it becomes reflected differently.*0465

*Really complicated question, so weâ€™re going to do a reasonable approximation.*0471

*Weâ€™re going to treat sound as if it spreads in all directions equally and simultaneously.*0475

*An outwardly radiating sphere, so that makes sense.*0479

*If weâ€™re on a clear plain, weâ€™re out somewhere in a grass land and we shout.*0482

*Its going to expand everywhere at once. Weâ€™re going to have some point source and itâ€™s going to burst outwards just in a continuing radiating sphere.*0487

*Remember, this is actually a sphere that itâ€™s bursting out in.*0494

*The point source and it blows out in all positions. Some of it may wind up being reflected but itâ€™s a reasonable approximation.*0500

*Not perfect, but it gives us something to hold on to and have an understanding of how sound works.*0505

*If thatâ€™s the case, whatâ€™s the surface area of a sphere?*0510

*Well the area of a sphere is equal 4 times pi times the radius of the sphere squared. 4 pi r squared.*0513

*If the center of an imaginary sphere is put on our emitter, so we have some imaginary sphere that weâ€™re considering.*0519

*We put it so that the center of that sphere is around the emitter. We are standing r away.*0526

*The intensity of the sound is going to be that area of the sphere dividing the power of our emitter.*0531

*The intensity will equal the power divided by 4 pi r squared.*0536

*The area divides the power. If weâ€™ve got that simplified version of the expanding sphere then weâ€™re able to use this nice little formula.*0541

*Intensity is a great way to measure sound as a quantitative thing, but itâ€™s not a very good way to talk about it.*0551

*The range of possibilities for human hearing is really, really large. 1 x 10^-12 watts per meters squared.*0558

*Sorry I should have mentioned that before. If intensity is equal to power over area.*0567

*Remember we talk about power as watts. Area, well we use for our unit of length, meters.*0571

*Area is going to be meter time meter or meters squared.*0578

*Intensity is equal to the watts divided by meters squared.*0582

*Human threshold for hearing is around 1 x 10^-12 watts per meters squared.*0585

*Thatâ€™s a really, really small amount that weâ€™re able to pick up.*0590

*The pain threshold is massively larger, 10^13 times more.*0594

*Pain threshold when we start experience real physical pain from the sounds going off around us is 10 watts per meters squared.*0598

*Thatâ€™s a really huge array of different possible values that weâ€™re able to pick up.*0606

*We might be able to talk about it intensity like this thing but our experience of sound isnâ€™t with each of these little tiny amounts different or these very large possible amounts different.*0610

*Our experience is actually based on a different scale. Itâ€™s based on a log rhythmic one.*0620

*We experience sounds multiplicatively, so thatâ€™s where the idea of decibels is going to come in.*0624

*To deal with this, weâ€™re going to introduce the idea of the decibel.*0630

*DB which uses a log rhythm to help us manage this vast range of possibilities.*0633

*If you donâ€™t remember what a log is. Youâ€™re going to want to go back and youâ€™re going to want to check either pre-calculus or calculus and get a real quick understanding of it.*0638

*The basic idea is log base a of x equals y. Means the same thing as x to the y equals, sorry, not x to the y. Screwed that up.*0645

*Log base A of x to equal to y, gives us a to the y equals the quantity x.*0662

*For example, log base 10, which is what weâ€™ll be using for the log rhythm for decibels.*0671

*Log base 10 of 10 equals 1 because 10^1 equals 10.*0676

*But log base 10 of 100 is equal to only 2 because 10 squared equals 100.*0684

*Similarly, 1,000, log 10 of 1,000 would be 3.*0690

*For simplicity weâ€™re just going to start saying log even though weâ€™re going to be talking about log base 10.*0694

*You could have the base of anything but weâ€™re going to be talking about log base 10.*0699

*For ease weâ€™ll just say log from here on out.*0703

*This is the important thing, if you donâ€™t know, weâ€™re going to wind up needing to use some of the properties that log rhythms have later on in the examples.*0705

*You might want to go back and refresh some of your memory on this.*0711

*On with decibels. Weâ€™re going to define the sound level beta, and this guy right here is called beta.*0714

*B E T A. Heâ€™s another one of our Greek letter friends.*0721

*The sound level beta, by referring to the â€˜I knotâ€™, the intensity, the basic intensity, the lower threshold of our hearing.*0725

*Weâ€™re going to utilize log. So beta, the sound level is equal to 10 decibels and that gives us a nice chunky number that we can hang on it.*0732

*10 decibels times log of the intensity of the sound that weâ€™re listening to divided by that base threshold I knot.*0740

*Log of I over I knot times 10 decibels gives us our sound level.*0750

*Notice, a rise in 10 decibels means 10 times the intensity because weâ€™re dealing with log 10.*0755

*If we go from 10 decibels to 20 decibels, that means the intensity has gone up by a power, not by a power of 10, has gone up multiplicatively by 10.*0761

*Because of log has gone from 1 to 2, it has gone up one number.*0770

*Going up one number we multiply by 10 decibels, so weâ€™re going to have a change in the power of 10 times that we started off with.*0775

*If we go from 100 decibels to a 110 decibels, the exact same thing going on, because itâ€™s a difference of 10 decibels.*0782

*That means our log creates a difference of 1, so itâ€™s times 10.*0788

*If we had a difference of 20 decibels, itâ€™d be a difference of a 100.*0792

*Sorry not a difference, a multiplicative 100.*0796

*100 times the power. If we had a difference of 30 decibels, itâ€™d be 1,000 times the power, etc., etc.*0799

*Remember, weâ€™re dealing with a log so itâ€™s going to be connected to how exponents work.*0806

*Youâ€™re going to have to remember how logs work. If you remember that, sorry to harp on it so long, but if you donâ€™t remember it right now, go back, relearn it really quickly.*0810

*It will make this understanding how decibels business work really, really easy if you compared to what youâ€™re standing with right now if you donâ€™t remember how logs work.*0816

*Hereâ€™s some loudness examples. A bunch of examples.*0825

*The example sound and the sound level that it gives you.*0829

*The auditory threshold for human hearing is at 0 decibels, because remember I over I knots.*0833

*If thatâ€™s equal to 1, log of 1 equals 0.*0838

*Light rustling leaves, very light, vague slight sound. 10 decibels.*0841

*A whisper, 20 decibels. Normal conversation gives us anywhere between 40 and 60 decibels depending on the loudness of the conversation.*0846

*A washing machine might come in around 50 decibels although itâ€™s going to depend on the washing machine.*0853

*Car at 10 meters, once again, depends on the type of car.*0858

*Hearing damage from long term exposure, so this just means that youâ€™re being exposed to something constantly and youâ€™re not using any sort of hearing protection.*0862

*Notice how many things are going to be above that. A busy highway at 10 meters. A chainsaw at 1 meter.*0868

*A rock concert. So if youâ€™re going to rock concerts regularly. If youâ€™re constantly using loud motor driven things.*0874

*Either working around large powerful engines, going to like a construction yard or doing any sort of serious construction work.*0881

*Youâ€™re going to definitely want wear hearing protection because youâ€™ll start to experience hearing damage.*0890

*If youâ€™re shooting at a range, youâ€™re definitely going to want to have at least one form of hearing protection on if not two forms of hearing protection.*0894

*Look at how incredibly high that is. 150-160 decibels, that means that weâ€™re a 1,000 times potentially or even more depending on the kind of gun being shot.*0900

*A 1,000 times the power of a pain threshold. Guns really, really powerful amount of noise coming out of them.*0910

*Any sort of explosion, really powerful amount of noise coming out it, youâ€™re defiantly want to wear some sort of hearing protection if youâ€™re around that sort of noise.*0918

*Keep in mind; anything thatâ€™s particularly loud can cause hearing damage over long term exposure or even short term exposure if itâ€™s very loud.*0926

*Youâ€™re going to want to keep that in mind because when you get older itâ€™s going to be a real disappointment when you start to lose your hearing.*0934

*Beats. So from earlier work we know that waves interfere with own another.*0942

*If the waves have the same frequency, the amount of constructive or destructive interference comes from how in or out of phase they are.*0947

*As they sync up, theyâ€™ll manage to make themselves louder but as they come out of sync theyâ€™re going to wind up becoming quieter as they become more and more destructive on one another.*0953

*What if theyâ€™re different frequencies? From before it was just a question of how out of phase that they are and that determined how much destructive or constructive interference we had.*0964

*What if theyâ€™re different frequencies? That means weâ€™re going to have the constructive interference, the amount that theyâ€™re syncing up is going to change as they cycle through their different frequencies.*0972

*They have a 1 hertz difference in their frequencies, every second theyâ€™re going to cycle from fully in phase to fully out of phase.*0981

*Weâ€™re going to experience the sense of them working together and then canceling one another out.*0990

*Working together and then canceling one another out. Thatâ€™s going to be called the beat frequency.*0994

*The beat frequency is equal to the difference between the two numbers. It doesnâ€™t matter which one is the larger one and which one is the smaller once because itâ€™s the absolute value.*0998

*Thatâ€™s how weâ€™re going to experience it. Itâ€™s going to just be the difference between the two numbers.*1007

*They waves will come in and out of phase based on the difference in their frequencies.*1011

*It doesnâ€™t matter if its 10 hertz and 11 hertz or a 1,001 hertz and a 1,000 hertz.*1015

*Thatâ€™s still going to be the same beat frequency from our experience.*1021

*Visualizing this and visualizing beats, drawing them out, really difficult potentially.*1025

*Theyâ€™re really easy to hear, so thatâ€™s how weâ€™ll demonstrate this one here.*1030

*In a few moments weâ€™re going to play an audio clip. The order of the clip will go like this; a 440 hertz pure tone just by itself.*1033

*Then a 445 hertz pure tune by itself. Now notice, these sound pretty darn close, these sound really alike.*1040

*If youâ€™re not good at hearing differences in small frequencies you might not even be able to notice it.*1049

*Itâ€™s just barely noticeable that these two things are different tones, but when we play them simultaneously right after that, 440 hertz and 445 hertz.*1054

*Weâ€™ll be able to really notice the fact that theyâ€™re not the same thing anymore. Weâ€™re going to notice a beat frequency of 5 hertz as they pull in and out of phase.*1066

*Weâ€™re going to hear that sound. The next one weâ€™ll play after that is 440 hertz compared to 441 hertz.*1073

*Youâ€™re going to hear a beat frequency of 1 hertz as they come in and out of phase.*1079

*Youâ€™ll hear the sound louder and then quiet down to nothing and then louder and then quiet down to nothing.*1082

*Then finally, weâ€™ll have the first frequency stay at 440 hertz and just remain there while the second one will slide from 441 hertz to 450 hertz over ten seconds.*1087

*Weâ€™re going to hear those beat frequencies go from 0 to 10 hertz.*1098

*Weâ€™ll hear that beat frequency of getting louder, getting quieter. Itâ€™s going to speed up over those 10 seconds as the beat frequencies become larger and larger and larger.*1101

*Okay, so weâ€™re going to listen to it and there we go.*1109

*Okay, now we have some idea of how those beat frequencies work.*1132

*The thing thatâ€™s really interesting to notice is how those two tones that donâ€™t really seem that different suddenly produce this really noticeable phenomenon in this beat frequency.*1136

*At 440 hertz and 441 hertz, heard on their own we wouldnâ€™t be able to notice the difference, but put right next to one another, put right on top of one another, not next to each.*1143

*Put right on top of another, suddenly that beat frequency becomes really, really noticeable.*1153

*Weâ€™re definitely able to hear those things. As the slide happens we start to hear those sounds change, we start to hear those beat frequencies change more and more.*1158

*In fact, you might have noticed at the very end, as the tail end of it. It starts to sound like the beat frequency is in some way its own sound.*1165

*Thatâ€™s kind of true. The beat frequency becomes perceived as its own sound as the two sort of fight one another and we get this extra sound that is the two working against one another or together.*1170

*Theyâ€™re creating this extra sound. Sound is a very complex phenomenon because once again weâ€™re hearing many, many different waves.*1182

*Itâ€™s easy to talk about as a single wave, but in real life weâ€™re hearing many, many different waves working together, working against one another all simultaneously.*1188

*Because weâ€™ve had a lifetime experience listening to sound, weâ€™re able to have an idea of how to turn all that auditory information into something we can actually process and operate on.*1195

*Once again, weâ€™ve had a lifetime experience; we know what these sounds mean.*1205

*But really, when we you get right down to it, itâ€™s a lot of very complicated information.*1209

*Itâ€™s because weâ€™re so good at understanding and analyzing. Weâ€™ve got brains and theyâ€™re developed to do this.*1213

*Theyâ€™re able to make sense, to get some meaningful information.*1218

*Finally, sonic boom. What happens when an object exceeds the speed of sound?*1222

*It moves faster than sound, producing a conical shockwave in its wake.*1227

*When you go past the speed of sound suddenly a lot of things are going to change.*1232

*Normally if youâ€™re moving slower than sound, the sound wave, the fact that youâ€™re pushing on the air in front of you tells the sound in front of it because itâ€™s basically translating that information through the speed of sound.*1236

*Tells it to get out the way, thereâ€™s this really fast guy coming. So itâ€™ll be able to create a moving pressure wave and youâ€™ll be able to sort of push the sound out of your way before you have to actually run into it.*1248

*Suddenly once youâ€™re moving faster than sound, youâ€™re movement is faster than the sound can propagate the information of your moment coming.*1260

*So youâ€™re actually slamming, you have toâ€¦your aircraft or spaceship has to be able to slam the air out of the way.*1267

*Youâ€™re actually slamming all of those molecules, so suddenly the fact that youâ€™re slamming all of these molecules, slamming all of these atoms out of the way.*1275

*There is going to be way more friction, way more drag, way more heat produced on your thing.*1283

*Whole bunch of complicated ideas to talk about here, but weâ€™re going to just talk about real quick, real simple idea.*1287

*Weâ€™re going to see the fact that every time you emit a sound or just the fact that youâ€™re going faster than sound is able to handle.*1293

*That information is emitted spherically out in a sphere from you, or a circle if weâ€™re looking two dimensionally.*1300

*The next time you emit it, you actually manage to already pass the edge of that expanding circle.*1306

*See over here, you emit here, but by the next time you emit, youâ€™ve already passed the edge of that expanding thing.*1312

*Itâ€™s a little harder to see over here because weâ€™re looking so far behind in time.*1319

*Over here where weâ€™re looking closer to the instant that this picture is taken, weâ€™re able to see the fact that the emitting of information happens after you passed the front of the information that youâ€™re coming.*1323

*Weâ€™re going to get this depending on the speed that weâ€™re moving, weâ€™re going to see this conical wave front out of you.*1337

*This sonic boom appearing and thatâ€™s what people on the ground or other people in the air would wind up hearing is that slamming of air getting transmitted to them.*1343

*That slamming of air can only move at the speed of sound, so youâ€™re able to actually get passed the sound of your own coming because youâ€™re going faster than the speed of sound.*1352

*Also if the speed of sound is vs and the object is traveling at v, we give it a Mach number.*1365

*V over vs. So Mach 1 is just the speed of sound, youâ€™re traveling at sound.*1370

*Mach 2 is two times the speed of sound because you have to be traveling double the speed of sound etc., etc.*1375

*Mach 5 would mean that youâ€™re managing to move at five times the speed of sound.*1381

*Really interesting ideas here but we really have quite enough understanding or time at this moment to tackle all of them.*1384

*But weâ€™re getting the chance to dip our toes in whatâ€™s going on here.*1391

*Weâ€™re ready for some examples. On a warm summer evening, the speed of sound in the air is 340 meters per second. If you see a firework explode in the air, so boom, firework explodes, and weâ€™re standing over here.*1395

*We see the firework explode almost instantly because light travels so incredibly fast as weâ€™ll talk about in the next section.*1408

*We seeâ€¦we can effectively pretend that itâ€™s instantaneous.*1416

*We see it explode the instance it explodes, but it takes some time for the sound to reach us.*1420

*It explodes and there is some distance between us and it. Itâ€™s going to take 4 seconds.*1424

*The speed of sound is 340 meters per second and the time that it takes is 4 seconds, we just figure out the distance is equal to the velocity times the time.*1433

*So 340 times 4 seconds and we see the fact that it must be 1,360 meters away from us because it takes time for that much distance to be crossed by those pressure waves coming from the explosion.*1445

*However light 1,360 meters is practically nothing to light. Light moves super, super fast as weâ€™re going to talk about in the next section.*1461

*Weâ€™re able to effectively treat it as moving over that distance as instantaneously.*1472

*If weâ€™re really, really far distance, light wouldnâ€™t necessarily at something that we can treat as instantaneous but the distance for the sound would be so incredibly far at that point that we pretty much wouldnâ€™t be able to hear it at all.*1478

*Example 2. If you double the intensity of a sound, what increase does that cause in decibels?*1489

*We start off with some sound at intensity I, what increase are we going to see in the decibels?*1495

*Say our old sound came in at b, so old intensity is as same as beta.*1500

*Then our new intensity is going to make beta new.*1509

*What is beta new? Beta new, remember, I new, intensity new is equal to 2 times I old, which for e, weâ€™ll just say I old equals i.*1515

*Because thatâ€™s what we had it as before. If we double the intensity, I, of a sound, what increases does that cause in decibels?*1530

*So I starts off being the same as beta and I new is going to be equal to beta new and I new equals 2 times i.*1537

*Beta new is equal to our formula for decibels is 10 decibels times the log base 10 of 2 I, because thatâ€™s the intensity of our sound, divided by I knot.*1544

*10 decibels times log base 10 of 2 times I over I knot, you canâ€™t stop me from separating that.*1562

*Still the same thing; either multiply it on the numerator, just multiplying the whole fraction, same thing.*1575

*Now, because the nature of log rhythms, we can separate those two. Log of xy is equal to log x plus log y.*1580

*At this point weâ€™ve now got log 10 of 2 plus, and we should multiply because remember that 10db has to go over the entire thing.*1590

*Plus log 10 of I over I knot. We spread that out, we distribute, we get 10db times log 10 of 2 plus 10db log 10 of I over I knot.*1602

*Or remember, log 10 of I over I knot times 10db, thatâ€™s justâ€¦thatâ€™s the general expression for what something has as a sound level, what something is in decibels.*1628

*If thatâ€™s what weâ€™ve got and we started off originally with I, then that means this whole thing on the right is just equal to our original beta. Beta old, right?*1639

*Our original beta is over here on the right and now we just have to figure out 10db times, well log base 10 of 2 is approximately equal to 0.301, plus that old beta.*1648

*That means 3.01 decibels plus the old number of decibels. The increase that we have is how much weâ€™ve added to the old number of decibels.*1666

*So our increase in sound is that 3.01 decibels. If you double the intensity, you donâ€™t experience a doubling in the number of decibels.*1679

*Not by a long shot. Youâ€™re just going to wind up adding on 3.01 decibels to the amount that you had originally.*1687

*Doubling the intensity does not mean doubling the decibels. Anything between intensity and decibels has to go through a log first.*1694

*We have to calculate this stuff out otherwise weâ€™re going to wind up tripping over stuff.*1701

*Now weâ€™re going to see something again about the importance of how much logs are going to play with this stuff by a slightly more complicated example.*1705

*Assume we can treat sound as an expanding evenly in all directions. So that same spherical idea we talked about before.*1712

*Itâ€™s not perfect but itâ€™s a pretty good approximation and just like when before when we got rid of air resistance.*1719

*Not perfect but often a good approximation for a basic physics idea.*1724

*If weâ€™re currently 1 meter from an emitter and we hear a sound at x decibels, what distance away from the emitter will lower the sound by 10 decibels, i.e. bring it to x-10 decibels?*1728

*To begin with, letâ€™s note the fact that the emitter, no matter what distance, the emitter is still going to be putting out p equals the power.*1739

*The intensity is equal to the power over the area and since weâ€™re dealing with a sphere, weâ€™ve got power over 4 pi r squared.*1752

*Now we can start using our decibels connection, so we know that for the new one that we want to create, we want to see the distance r that we have to be at.*1764

*What distance r will create x minus 10 decibels. Our formula, 10 decibels and for ease, Iâ€™m just going to drop the base but we still know Iâ€™m talking about log base 10.*1774

*Of the power, divided by 4 pi r squared. Now power doesnâ€™t change because power is constant for this emitter, is going to be equal to x minus 10 decibels.*1785

*Whatever we started with, lowered by 10.*1796

*If we want to know what this is, we know what x is, right?*1798

*X was the original amount. So letâ€™s write everything in again so we can keep our equation proper.*1802

*X, x was the original number of decibels. So the original number of decibels was what the original r was.*1813

*Our old r was 1, right? We used to be 1 meter away from the sound source, so itâ€™s going to be pi times 1 square minus, then we have to keep going up from what was above, 10 decibels.*1818

*Now at this point, that means weâ€™ve got 10 decibels showing up everywhere.*1835

*This becomesâ€¦we divide by 10 decibels, these cancel out here and here and this becomes 1 right here.*1840

*At this point we can now do something else. Once again, if you donâ€™t remember too much about logs, youâ€™re going to want to double check, I mean youâ€™re going to want go back, relearn this really quickly.*1848

*We can cancel out a log by raising it to whatever the power of the base is.*1858

*In this case, since we know those two sides are equal, 10 to each of those sides would still be equal.*1863

*So we raise both sides with a power underneath of 10. So 10 to the log p over 4 pi r squared is equal to 10 to the quantity log power over 4 pi, because 1 squared is just 1, minus 1.*1867

*Now 10 to the log, that cancels out and we get whatâ€™s inside, p over 4 pi r squared equals p over 4 pi.*1886

*One thing to notice is that weâ€™ve got 10 to theâ€¦we can separate it, 10 to the xy is equal to 10 to the x times 10 to the y.*1901

*It just getsâ€¦Sorry, 10 to the x plus y. Misspoke there.*1909

*10 to the x plus y is equal to 10 to the x times 10 to the y because we just add things together.*1912

*X squared times x becomes x to the 2 plus 1 x cubed.*1918

*We have to remember that and weâ€™ve got still over here, 10^-1 because weâ€™re separating those two different things.*1923

*At this point we can now cancel p over 4 pi from both sides and what weâ€™ve got now is 1 over r squared equals 1 over 10.*1929

*At that point, weâ€™ve got r squared equals 10, so r is equal to the square root of 10, which is approximately equal to 3.16 meters.*1943

*So notice that because the way we did this, this whole thing occurred on the fact that we were dealing with r squared over here, here right.*1963

*If instead of starting at 1, weâ€™d start it at r old, that r old would still have shown up over here and we would have had that.*1973

*What it is; is itâ€™s not just going 3.16 meters away. Itâ€™s not that at all, its 3.16 meters times whatever the original distance was.*1981

*Itâ€™s our original distance times 3.16. So in our case, we looked at a slightly easier one because we dealt with an initial distance of 1 meter, but we can also expand it to a slightly more complicated thing.*1990

*Itâ€™s actually route 10 times the original distance that we started at if we want to get a 10 decibel lower.*2001

*Lowering it by 10 decibels means multiplying our original distance by route 10, which is why we get going from 1 meter to 3.16 meters.*2008

*Say we started off at 5 meters and we wanted to lower it by 20 decibels, then weâ€™d have to take that 5 meters originally, multiply it by route 10 twice.*2017

*Route 10 twice, becoming 10, so weâ€™d have to go from 5 to 50 meters if we wanted to be able to get a 20 decibel lower in the sound.*2026

*Itâ€™s important to note, once again, dealing this stuff can be a little confusing at first because weâ€™re dealing with logs.*2036

*Youâ€™re definitely going to want to work on calculating this thing out by hand because you might be surprised by how some of the results are going to work out.*2042

*Think about this, the fact that weâ€™re going from 1 meter to 3.16 meters to get a lower of 10 decibels might not be inherently oblivious at first because weâ€™re working with the way log rhythm works.*2047

*Log rhythm can be a little, a little new, a little odd at the first time youâ€™re dealing with it because weâ€™re normally canâ€¦weâ€™re normallyâ€¦the way we understand the world first is through additive understanding.*2058

*Adding things together. It is a little bit more difficult to think in terms of multiplication through exponents and thatâ€™s how logs look at the world.*2070

*Definitely the sort of thing, I definitely want to caution you if you have to do a problem with decibels, make sure youâ€™re working through the formula of how we get decibels first.*2078

*Otherwise itâ€™s really, really easy to wind up making mistakes.*2085

*Final example, a nice easy example to finish things off with.*2088

*Say we have a 256 hertz tuning fork and we put it to a violin and we hear a beat frequency of 3 hertz.*2092

*What are the possible frequencies that the violin is emitting?*2101

*Remember, f beat is equal to the difference in those two things.*2103

*If weâ€™ve got a 250 hertz tuning fork and weâ€™re comparing it to the frequency of the violin and weâ€™ve got 3 hertz beats coming out, then the two possibilities for the violin are the two things that are 3 away from 256.*2110

*Weâ€™ve got the frequency of the violin, it must currently be emitting. The violin can emit many things but weâ€™re going to treat it as if youâ€™re just bowing on a single thing, at a single tension.*2127

*At this point, weâ€™re going to see the two possibilities are 253 hertz, the lower one or 259 hertz.*2136

*The two things that wind up being 3 hertz away from what weâ€™re comparing at.*2146

*Thatâ€™s how beats frequencies work if you need to solve anything with beat frequencies.*2152

*Once again, if youâ€™re not used to logs, go back, definitely going to behoove you to take 20 minutes just refreshing yourself on how logs work.*2155

*Otherwise some of this is going to be really, really complicated to understand how decibels work to solve any problems with it.*2162

*If youâ€™re working with decibels, definitely want to work through it, otherwise you can easily trip yourself up.*2166

*You want to remember everything is based on multiplicative ideas.*2172

*Thatâ€™s how you want to be approaching it through log rhythmic scale.*2175

*Alright, hope it made sense. Hope you have a better understanding of how sounds work and next time weâ€™ll wind up talking about light waves. Thanks.*2178

0 answers

Post by Peter Ke on April 5 at 07:00:14 PM

At 32:09, why is it 10^-1 and not -1?

1 answer

Last reply by: Professor Selhorst-Jones

Mon Feb 25, 2013 9:31 PM

Post by Valentina Gomez on February 25, 2013

I found this lecture quite interesting! Thank you for facilitating physics! It's not an easy task :)

1 answer

Last reply by: Professor Selhorst-Jones

Mon Dec 10, 2012 12:52 PM

Post by Meda N on November 30, 2012

How do I calculate the intensity of a sound wave measured in dBSPL?