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Ch 19: Waves & SoundWorksheetSee all chapters
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Intro to Waves
Wave Functions & Equations of Waves
Velocity of Transverse Waves (Strings)
Wave Interference
Standing Waves
Sound Waves
Standing Sound Waves
Sound Intensity
The Doppler Effect

Concept #1: Beats


Hey guys, in this video we're going to talk about beats and beat frequency beats are things that appear due to interference between two sound waves that occupy the same space at the same time so this is just another topic on interference which we've talked about a bunch of times before, Alright let's get to it. When two sounds occupy the same place at the same time they interfere, just like any two waves occupy the same place at the same time alright. Now I drew two sound waves right here this I put Y verses T but that should technically be pressure versus T because sound is a longitudinal wave it doesn't have a vertical displacement, and they have very slightly different frequencies as you can see. Because they start sort of in phase and then eventually they're out of phase and then they're sort of back in phase and then they're out of phase again. That forms this looking graph right here alright this piece right here where the interfered wave has 0 displacement in the pressure graph. A maximum displacement and then back to 0 this is referred to as a beat, and if I were to draw these over many many many many different cycles many periods you would see multiple of these beats continue to reappear you can see half of a beat right here and then you have the other half of the beat over here.

Now there's a few waves composed or repeating units like I said called beats, beats have two components you have a high frequency component where you can see the rapid oscillation going on within the beats but beats also have a low frequency component which is the beats themselves. Alright you can see that how long it takes for a whole beat to occur this period right here, this period right here it's obviously a much much larger period then the period of these tiny oscillations in here which occur much much more rapidly and thus have a much much smaller period. The smaller the period the larger the frequency, so beats are composed of those two things a low frequency component and a high frequency component the low frequency component which is known as the beat frequency is given by the difference in the two frequencies that make up the beats the reason why beat frequency is important is because remember the intensity of sound is dependent upon the largest pressure, the maximum pressure right the intensity looks something like one half times the maximum pressure divided by the density times the speed so the larger the pressure the larger the intensity so the loudest sound in this beat is going to be the sound right here at that peak intensity. So notice how long does it take between those really really loud sounds that's the low frequency part that we were talking about, so the low frequency part is the part that we care about because that's when you hear the sound. Now that occurs at this frequency F1 minus F2.

Remember each beat is a point of maximum displacement so the volume of sound is directly related to this large pressure as I said this is a point where the sound is loudest. What the listener hears is called the beat frequency is kind of like a waaa waaa waa sound those waaaas those are the high pressure loud parts to the beats where you'll have beats that look like this or they have a high frequency component. But what you hear are those maximum pressure points and those are the low frequency components these have the large period where the frequency is given by F1 minus F2 but the absolute value because you can't have negative beat frequencies. Let's do an example to illustrate this point, the tuned low E string on a guitar emits a sound at 82 hertz if you were to strike a tuning fork which emitted a sound at exactly 82 hertz, and you plucked your untuned low E string, you hear a beat frequency of 4 hertz. What possible frequencies could your untuned low E string be at? So you want to get it from whatever its untuned frequency is to the properly tuned frequency and this is the most popular way to tune a guitar is to play a sound or really any string in the instrument and possibly any instrument is to play a sound that you definitely know to be the correct tone the correct frequency. Play the untuned note and listen for the beat frequency and adjust until there's no more beat frequency but for now our beat frequency is 4 hertz. That means that there are two possible values it could either be 82 plus 4 which is 86 hertz or it could be 82 minus 4, which is 78 hertz this comes from the equation for beat frequency remember that beat frequency is the absolute value of F1 minus F2. 82 and 86 are separated by 4, but 82 and 78 are also separated by 4 so these are the two possible frequencies it could be at without changing anything to the problem leaving the problem exactly as it is you cannot possibly know which of those two frequencies is the right one. Alright guys that wraps up this introduction to beats and beat frequency. Thanks for watching.

Practice: A string emits an unknown sound. You strike a tuning fork which emits a sound at EXACTLY 300 Hz, and you hear a beat frequency of 20 Hz. You then tighten the string, increasing the tension in string. After you pluck the string and strike the tuning fork, you hear a new beat frequency of 30 Hz. What is the unknown frequency of the string, originally?