(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 will observers hear who are located, at rest,

(b) due south, of the whistle?

Accepted Answer

Hey, everyone in this problem, we're told that the fog horn of a stationary ship emits a sound at a frequency of 300 Hertz. The wind blows at 20 m per second from the west heading east. Given that the temperature is 20 °C, we're asked to determine the frequency heard by stationary observers located east of the stationary ship. We're given four answer choices all in Hertz option A 280 option B 300 option C 330 option D 350. Now let's kind of draw out a picture of what we have going on. So what we have is our ship and we have our observers located to the east of our ship. So we're gonna draw that to the right. So these are our observers and we know that the wind is traveling to the east from the west. So it's going in the direction from the ship to the observer. Now, the frequency emitted by the ship we know is 300 Hertz and we wanna know the frequency heard by the observer. Now this is a Doppler effect type of problem, but we have this added kind of difficulty of the wind. Now, when we have a Doppler type effect problem, what we're going to do as we always take the direction from the observer to the ship as our positive direction, we can go ahead and do that. Now. And in this case, because we have wind and when we're using this equation, we wanna consider wind constant. So what we're gonna do is actually consider a reference frame where the wind is stationary. OK. So if the wind is stationary, then what that means is the velocity of the ship itself will be equal to 20 m per second. And the velocity of the observer will also be equal to 20 m per second. And the wind is traveling to the right 20 m per second. And so the ship and the observer, if we take that wind to be stationary is going to be 20 m per second. So moving to the left 20 m per second. OK. All right. So what we can do now is think about the Doppler effect equation. And what that tells us is that the frequency heard by the observer will be equal to the speed of sound colos speed of the observer divided by the speed of sound plus the speed of the source. And all of that is multiplied by the frequency of the source. So we now have V nat and vs but what about this value V we call that this value V. The speed of sound depends on the temperature of the air that it's traveling through. And recall that we have the equation where V is equal to 331 plus 0.6 T meters per second. And in this case, we're gonna have the is equal to 331 plus 0.6 multiplied by 20 meters per second, which gives us a speed of sound of 343 m per second. In this case, in that 20 degree air. OK. So we have everything now we need for our equation. So we can say that the frequency the observer hears is going to be equal to 343 m per second. What's 20 m per second, divided by 343 m per second plus 20 m per second multiplied by that initial frequency, the frequency um emitted by the ship. Now what you'll notice because VN and BS are equal the numerator and denominator of the first term in this equation are going to be the same. So when we divide them, we just get one which tells us that the frequency the observer hears is just equal to the frequency that the ship actually emits. And we know that that's equal to 300 Hertz. OK? So that frequency heard is going to be the exact same. And this is true when we're dealing with the wind in general, they both the source and the listener are stationary and we have wind. This is gonna be the case. And there's a couple different ways we can see this. We chose to do it by looking at these velocities, relative velocities and taking a different reference frame. We can also think about looking at the wavelengths of the sound as well and figuring it out that way and no matter which way you do it, you're gonna get that these frequencies are the same, taking a look back at our answer choices we can see now that option B is going to be correct and the frequency heard by the stationary observers is 300 Hertz. Thanks everyone for watching. I hope this video helped see you in the next one.

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 will observers hear who are located, at rest,
(b) due south, of the whistle?

Watch next

The Doppler Effect practice set

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 will observers hear who are located, at rest,(b) due south, of the whistle?

Watch next

The Doppler Effect practice set

(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 will observers hear who are located, at rest,
(b) due south, of the whistle?