(III) A factory whistle emits sound of frequency 770 Hz. The w...

Question

(III) A factory whistle emits sound of frequency 770 Hz. The wind velocity is 15.0 m/s from the north (heading south). What frequency is heard by a cyclist heading

(f) west, toward the whistle at 12.0 m/s? Assume T = 20 °C .

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice prom together. So first off, let us read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem. A musician is playing a note of frequency 450 Hertz on a stationary loudspeaker. The wind is blowing at a velocity of 14 m per second from the west to the east, calculate what frequency the note would appear to be to an observer heading south toward the loudspeaker at a velocity of 20 m per second, assume that the temperature T is equal to 25 °C. So that's our angles. We're trying to figure out what the frequency of the note would be when it's considered from the perspective of an observer heading south towards the loudspeaker at a velocity of 20 m per second. And if the temperature of air is 25 °C, so that's our angle, we're ultimately trying to figure out what the f frequency is given these specific conditions. Awesome. So looking at our multiple choice answers, we can see that all of them are in the same units of Hertz, which is the standard unit of measurement for frequency. So let's read them off to see what our final answer might be. A is 420 B is 430 C is 450 D is 480. Awesome. So first off, we need to note that the source frequency or the source of the noise is stationary. Therefore, we could write that the speed which we're gonna call the SRC is equal to 0 m per second. Is it something stationary? It's not moving? So it's 0 m per second. Let us also note that the wind blows west to east, so west to east, whereas the observer moves towards the south, so the wind blows, so west to east equals wind and observer, which I'm just gonna put o equals south since the observer o which to get. So we don't get confused, I'll call it ob so the observer equals it moves to the south or towards this up. So therefore, we need to note that the wind speed will not affect the speed of sound since the wind blows in a direction that is perpendicular to the direction of the velocity of the d of the observer, which is, is very important. So I'll say it again. So the wind speed will not affect the speed of sound in this particular case, because the wind blows in a direction that is perpendicular to the direction of the velocity of the observer. Therefore, in this case, the observer is moving towards the stationary source with a speed of. So let us note that the velocity of the observer which are called vo is equal to 20.0 m per second. Awesome. Or in this case, since in our problem itself, it just says 20 m per second. Let's just keep things simple and just call it 20 m per second, Just you know, keep everything, you know, simple straight to the point. And then, so we can also recall the equation help us solve for the speed of sound at a given temp at a given temperature. So let us note that the speed of sound, that's what's called as, vs the speed of sound is equal to, let's recall and use our equation 331 plus 0.6 multiplied by T where T is the temperature. In this case, the temperature is given to us as 25 °C. So let's solve for vsvs is equal to 331 plus 0.6 multiplied by 25 °C. Which will mean that vs in this case will be equal to when we plug it into our calculator 346 m per second. And let us note that the original frequency solved a little and symbol and the original frequency F is equal to 450 Hertz. So now we need to recall and use our apparent frequency equation which states that F prime is equal to F multiplied by VS plus V divided by, VS minus VSRC. So now we can plug in all of our known variables to solve for F prime. So let us note that F is equal to 450 Hertz multiplied by RVS which is 346 m per second plus RV, which is 20 meters per second, divided by 346 m per second minus 0 m per second. So when we plug that into our calculator, we will find that F prime, which is our final answer that we're trying to solve for is equal to 476 0 476.01 hurt, which is approximately equal to 480 Hertz when we round to the nearest hole number. And that's it. That's our final answer. Hooray. We did it. So looking at our multiple choice answers, the correct answer has to be the letter D 480 Hertz. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Struggling with Physics?

(III) A factory whistle emits sound of frequency 770 Hz. The wind velocity is 15.0 m/s from the north (heading south). What frequency is heard by a cyclist heading
(f) west, toward the whistle at 12.0 m/s? Assume T = 20 °C .

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