Music Mystery: 2(Vsound) for the 2nd Harmonic?

[vetgirl1990]

Homework Statement

A guitar player is plucking a strong of length 30cm. How fast must the player move towards or away from the stationary observer, in order for the observer to mistake the fundamental frequency for the second harmonic?

ANSWER: 2(Vsound) towards the observer

Homework Equations

Frequency for string fixed on both ends: f = 2n/vL
Doppler effect for source moving towards stationary observer (observer will hear higher frequency):
f" = v_sound / v_sound - V_source

The Attempt at a Solution

f = 2n/vL = 2(1) / 343(0.3) = 205.8 Hz for the fundamental frequency --> set as f in the doppler equation
f = 2(2) / 343(0.3) = 411.5Hz for the second harmonic --> set as f" in the doppler equation

411.6 = 343 (205.8) / (343-v_sound)
V_sound = 171.5 m/s = 1/2 v_sound

I am getting 1/2 the speed of sound, rather than 2x the speed of sound which is the answer. What am I doing wrong?

 

[haruspex]

I am getting 1/2 the speed of sound, rather than 2x the speed of sound which is the answer. What am I doing wrong?

Twice the speed of sound is clearly nonsense. The observer would not hear the player approach. Must be a typo.
Your answer looks right.

 

[vetgirl1990]

Twice the speed of sound is clearly nonsense. The observer would not hear the player approach. Must be a typo.
Your answer looks right.

LOL thank you! My initial reaction to the "answer" was that it was an extremely hypothetical situation. Thanks for verifying!