What Are the Highest and Lowest Frequencies Heard Due to the Doppler Effect?

[TheStig]

Doppler effect homework problem help (still lost)

Homework Statement

A block with a speaker bolted to it is connected to a spring having spring constant k = 17.0 N/m, as in Figure P17.40. The total mass of the block and speaker is 44.00 kg, and the amplitude of this unit's motion is 0.475 m. Assume that the speed of sound is 343 m/s.


(a) If the speaker emits sound waves of frequency 420 Hz, determine the highest and lowest frequencies heard by the person to the right of the speaker to the nearest 0.01 Hz.

Homework Equations

d = mg/k
vs = gt
[v/(v (+ or -) vs)]*f

The Attempt at a Solution

When my friend and I were working on this, here's what we did:
Got variables:
k = 17N/m
mass = 44kg
amplitude = .475m
v = 343m/s
freq = 420Hz
I = 1000Hz

Our way of solving was using k = mg/d and solving for d.
d = mg/17
d = 25.36 = 1/2 * 9.8 * t^2
t = 2.28


From here, we used the formula [v/(v (+ or -) vs)]*f.

My answers are 449.27 Hz and 394.36 Hz
Now, here's the problem, our answers end up being within 10% but we have no idea what we did wrong and any ideas as to how to get the correct answer from here. Thanks for any suggestions.

 

[TheStig]

Is there something I'm missing that is causing my answer to be about 10% off?

 

[m2003]

The Doppler effect is a phenomenon that occurs when there is relative motion between the source of a wave and the observer. In this problem, the speaker is attached to a spring and is moving back and forth, causing a change in the frequency of the sound waves it emits. The key equation to use in this problem is the Doppler effect equation, which is [v/(v (+ or -) vs)]*f, where v is the speed of sound and vs is the velocity of the source.

Based on the given information, it seems like you have correctly determined the velocity of the speaker using the equation d = mg/k. However, the next step would be to use this velocity to calculate the frequency shift using the Doppler effect equation. It looks like you may have used the initial frequency of 420 Hz in your calculations, which is not correct. Instead, you should be using the frequency shift, which is equal to the change in frequency from the original frequency of the sound waves.

To calculate the frequency shift, you can use the equation vs = gt, where g is the acceleration due to gravity. Once you have the velocity of the speaker, you can plug it into the Doppler effect equation to calculate the highest and lowest frequencies heard by the person to the right of the speaker. Remember to use the correct sign for vs (positive or negative) depending on the direction of motion of the speaker.

I hope this helps clarify the problem. If you are still having trouble, I suggest breaking down the problem into smaller steps and making sure you are using the correct equations and variables. It can also be helpful to draw a diagram to visualize the situation. Good luck!