[a] A flagpole consists of a flexible, 2.77 m tall fiberglass pole planted in co

Question

[a] A flagpole consists of a flexible, 2.77 m tall fiberglass pole planted in concrete. The bottom end of the flagpole is fixed in position, but 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 fiberglass is 2730 m/s?

________ Hz

[b] 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?

a) 2nd
b) 3rd
c) 4th
d) 5th

Explanation / Answer

Length of the flagpole l = 2.89 m

speed of the wave in the glass fibre v = 2730 m/s

f = v [n / lambda]

for lowest frequency n= 1

wavelength of the wave lambda = 4 l

f = v / 4 l = 2730 / (4 * 2.89)

f = 236.16 Hz

------------------------------------------

f' = n f

1.01 KHz = n(236.16)

n = 1.01 KHz / 236.16

n = 4.28

Therefore lowest harmonic that the mouse can hear is

n = 4th

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