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A person leaning over a 125 -m-deep well accidentally drops a siren emitting sound of frequency 2500 Hz. Just before this siren hits the bottom of the well, find the frequency and wavelength of the sound the person hears (a) coming directly from the siren, $($ b) reflected off the bottom of the well. (c) Whatbeat frequency does this person perceive?

a) $f_{L}=2186 \mathrm{Hz} \quad, \quad \lambda=0.157 \mathrm{m}$b) $f_{L}=2920 \mathrm{Hz} \quad, \quad \lambda=0.118 \mathrm{m}$c) $f_{\mathrm{bent}}=734 \mathrm{Hz}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Cornell University

University of Washington

Simon Fraser University

Hope College

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So we first need to find the velocity of the Simon right before he hits the ground. So we know that the frequency of the listener equals the velocity plus the velocity of the listener divided by the velocity plus the velocity of the source times If you can see the velocity of the source rather, we're gonna use automatics in order to find the speed of the siren right before hits the ground. So we can say that b y final squared equals the y initial squared plus two g delta y. We know that the initial velocity zero So we can say that the final velocities equaling radical to G y to ji Delta wine So v y final equals the square root rather making to say two times 9.8 times the change in height. So 125 meters and then also the 1/2 power essentially taking a square root and this illegal 49.5 meters per second and this would be for the siren right before hits the ground. Um where we also using the velocity of sound in air So 344 meters per second. Actually, we're just he notices be so it would be a sound in there, so Ah, we ever givens OK. And after this for party, they want the frequency and the wavelength from the siren directly. Um, so the frequency of the listener, he This is simply the person on the top of the building and this is going to be equal to V plus 49.5 on V is the numerator and time's the frequency of the source so we can actually solve on directly and say 344 plus 49.5 times, 344 times 25 100. So that was the frequency of the siren. And this is the frequency is heard by the person. On top of the building is 2,186 hertz And then if you wanted to find this wavelength, this will simply be vey over the frequency. So this would be 344 divided by 2,186 and this is giving us 0.157 meters. So this would be your answer for the wavelength. And then this would be your answer for the frequency heard by the listener or, in this case, the frequency heard by the person on the top of the roof. Now, for part B, it's asking us for the frequency on the wavelength heard by the person. However, this is the the bottom of the well. So the sound is coming from the siren bouncing off the bottom of the well and then returning back to the listener on the top of the building. In this case, the person that is on the top of the building. So we have here the ah, we can say that the water here serves as the listener and we can say that the frequency of the listener equals the minus 49.5 thie times the frequency of the source. And this was equaling, um 3 44 divided by 3 44 minus 49.5 times the frequency of the source. So again, 25 100 hertz. And this is giving us all right. 2,920 hertz. So when the water serves as a listener, the frequency actually increases. So we can say also the wavelength here would be of the listener would be also equal to feed a lot of plate the frequency of the listener. So 344 divided by 2,920 this is equaling 0.118 meters. So this Abeer answer for part B and the report see, they're asking us for the beat. So, essentially, how many beats per second you here? Given this given these differing frequencies, so simply be f someone minus f sub to the absolute value of that, someone minus adds up to this is simply gonna be equal to 2,920 minus 2,186. And the frequency of the beat is going to be 734 hertz. So 734 beats per second. That is the answer for part. See, that is the end of the solution. Thank you for watching

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