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$\bullet$ Musical scale. The frequency ratio of a semitone intervalon the equally tempered scale is $2^{1 / 12}$ (a) Show that this ratio is$1.059 .$ (b) Find the speed of an automobile passing a listener at rest in still air if the pitch of the car's horn drops a semitone between the times when the car is coming directly toward himand when it is moving directly away from him.

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9.857 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

Lectures

08:15

In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Humans can only hear sound waves as distinct pitches when the frequency lies between about 20 Hz and 20 kHz. Sound above 20 kHz is known as ultrasound and has different physical properties from sound below 20 kHz. Sound waves below 20 Hz are called infrasound. Different species have different hearing ranges. In terms of frequency, the range of ultrasound, infrasound and other upper limits is called the ultrasound.

04:49

In physics, a traveling wave is a wave that propogates without a constant shape, but rather one that changes shape as it moves. In other words, its shape changes as a function of time.

02:55

The frequency ratio of a s…

02:33

(II) If a speaker mounted …

01:28

With what speed (km/h) doe…

02:16

Two cars are moving toward…

01:53

The horn of a car emits so…

01:57

Two cars have identical ho…

02:18

01:06

In the equally tempered sc…

03:21

So we're going to say the velocity of the listener equals zero meters per second and we know that the car is traveling to the right. So that means that the direction from the listener to the sources positive we can say direction from L Tu es is listener to source is positive. Now, at this point for party, they want us to see that one. What's the value of two to the one twelve 12? This is simply the 12th route of two, and it's going to be equal to 1.59 so you can simply plug this into a calculator. There's no really way to do this. You could multiply 1.59 12 times. And it will equal, of course, too. Um, however, yeah, you just have to plug this into a calculator to find the actual value. So for Part B, we're trying to find the velocity of the car so we can say that for part B, the velocity of the source is going to be equal to the native velocity of the car so we can say that the frequency of else of one is going to be equal. Teo the divided by V minus visa car times the frequency of the source. And this is the case of the car approaching. Now we can say that the velocity of the car equals now the velocity of the source equals the velocity of the car. This would be for the car approaching, and in fact, let's get a new workbook for this. So velocity of the source equals velocity of the car. So the positive velocity of the car, this would be, of course, the car is moving away. So the frequency of the listeners up to would be equal to the velocity divided by the velocity plus the velocity of the car times the frequency of the source. So we can say that the frequency of the listeners of one divided by the frequency of the listeners up to will simply be equal to 1.59 so to to the one twelve 12 power. And this will be equal to the the velocity divided by the velocity minus the of velocity of the car times the frequency of the source. And this is going to be divided by again. Ah, velocity plus the velocity of the car the denominator on velocity for the numerator, um, times again, the frequency of the source. So at this point, we know that this is going to cancel out. These were going to cancel out, and we're getting that 1.59 equals the velocity plus the velocity of the car divided by the velocity minus the paucity of car. Ah, here the velocity is the speed of sound through air. And we can say that 1.59 V minus 1.59 velocity of the car will be equal to the velocity plus the philosophy of the car. So you can say that the velocity of the car is going to be equal finally to 0.59 velocity of the speed of sound through air. Let's make this a little bit smaller and divided by 2.59 and this of equal point 0287 v or this will. The velocity of the car is going to be equal to 0.287 times 344 meters per second, and me find the philosophy of the car to be 9.9 meters per second, so that would be the final answer. That is the end of the solution. Thank you for watching.

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