A tall flagpole of height 5.99 m is made of a slightly flexible steel pole fixed

Question

A tall flagpole of height 5.99 m is made of a slightly flexible steel pole fixed in the ground. The top end of the flagpole is free to move. What is the lowest frequency standing wave that can be formed on the flagpole, if the wave propagation speed in the steel is 2730 m/s? Suppose that a standing wave on the flagpole gives rise to a sound wave of the same frequency. A person would be able to hear the sound produced by the above standing wave, since the average human being can detect sounds at frequencies between 20.0 Hz and 20.0 kHz. A nearby mouse, however, can only detect frequencies between 1.01 kHz and 90.0 kHz. What is the lowest flagpole harmonic that the mouse can hear?

Explanation / Answer

1.
fn = (2n+1)*V/4*L
lowest frequency will be for n=0
f1 = V/(4*L)
= 2730/(4*6.34)
= 107.65 Hz
Answer: 107.65 Hz

2.
fn = (2n+1)*V/4*L
fn = (2n+1)*107.65
for n=2, f2 = 5*107.65 = 538 Hz . Can't be heard
for n=6, f6 = 13*107.65 = 1400 Hz =1.4 KHz. Can be heard
for n=10, f10 = 21*107.65 = 2260 Hz =2.26 KHz. Can be heard
for n=11, f11 = 23*107.65 = 2476 Hz =2.476 KHz. Can be heard
Mouse can hear 6th harmonics which is lowest in given option
Answer: 6th

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