Simple Harmonic motion and Doppler effect question

[Xelb]

Homework Statement

So you're being pushed on a swing by someone who is whistling at a constant 60Hz. At the bottom, Vmax is 4 m/s. Explain what you hear as you swing toward and away from the source of whistling (speed of sound is 343 m/s for this problem).

Homework Equations

Observed frequency for someone moving toward and away from the source (I calculated the numbers correctly, it's the explanation that needs work).

The Attempt at a Solution

I said that we know that at the bottom, you're moving at 4 m/s, so you can calculate the doppler shift only at that point. These shifts are 60.7Hz moving toward the source and 59.3Hz moving away from it. This demonstrates that, at this bottom point, you hear a higher frequency moving toward the source and a lower frequency moving away from it.

This is my explanation so far, but I also need to account for the all of the other points in between and not just the bottom point and how the frequency varies in between. How can I do this?

 

[Sunil Simha]

I said that we know that at the bottom, you're moving at 4 m/s, so you can calculate the doppler shift only at that point. These shifts are 60.7Hz moving toward the source and 59.3Hz moving away from it. This demonstrates that, at this bottom point, you hear a higher frequency moving toward the source and a lower frequency moving away from it.

This is my explanation so far, but I also need to account for the all of the other points in between and not just the bottom point and how the frequency varies in between. How can I do this?

Actually, Doppler shift can be calculated for all other points provided you know the velocity at that point. From what I have understood in my class, the formula for Doppler shift is :

$f=|f_0\frac{v-v_o}{v-v_s}|$
where v-v_o, v-v_s are actually the vector difference in the velocities of the sound and the observer and the sound and source respectively. You have to take their modulus in the equation for frequency.

 

[tiny-tim]

Hi Xelb!

I'll add that, from the title to the question, you can presumably assume that the motion is shm.

 

[Xelb]

Actually, Doppler shift can be calculated for all other points provided you know the velocity at that point. From what I have understood in my class, the formula for Doppler shift is :

$f=|f_0\frac{v-v_o}{v-v_s}|$
where v-v_o, v-v_s are actually the vector difference in the velocities of the sound and the observer and the sound and source respectively. You have to take their modulus in the equation for frequency.

I only said you could calculate the doppler shift at this point because that's the only point where we are given velocity. At all the other points, I sort of have to guess what the frequency would be. I said that at the highest point that's closest to the source (the whistler) would be 60 Hz and that at the point farthest away from the source I said 58.6 Hz. At this point I'm just slightly confused as to how I can get these numbers. My physics prof said you can despite not knowing the velocity. I need to explain how the frequency varies at all of the points but I just don't know how...

 

[Sunil Simha]

Are you given the length of the swing? ( I mean the distance between the axis of rotation and the center of mass of the person)

 

[Sunil Simha]

At highest point, the velocity of the observer is zero and hence the observed frequency is same as the source frequency.

 

[Xelb]

Are you given the length of the swing? ( I mean the distance between the axis of rotation and the center of mass of the person)

Nope!

At highest point, the velocity of the observer is zero and hence the observed frequency is same as the source frequency.

I didn't forget to mention this (that the observed frequency would be 60Hz at the highest point). However I'm not entirely sure how to go about calculating the observed frequency at the completely opposite side of the highest point without a length.

 

[Sunil Simha]

I didn't forget to mention this (that the observed frequency would be 60Hz at the highest point). However I'm not entirely sure how to go about calculating the observed frequency at the completely opposite side of the highest point without a length.

I didn't understand what you meant by the opposite side of the highest point.

 

[Xelb]

I didn't understand what you meant by the opposite side of the highest point.

Say at point 5 is where you hear the frequency of 60Hz...but what about point 1? That's what I meant. Sorry if I wasn't clear enough.

 

[Sunil Simha]

Say at point 5 is where you hear the frequency of 60Hz...but what about point 1? That's what I meant. Sorry if I wasn't clear enough.

At point 1 too, the velocity is zero isn't it? So the frequency at point 1 would still be 60 Hz.