1. A flagpole consists of a flexible, 5.99 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? 2. 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. 10th.
c. 6th.
d. 11th.

Explanation:

The flagpole will act as closed organ pipe . If λ be wavelength of wave produced ,

n x λ / 4 = L where L is length of pole . n is odd integer like 1 , 3 , 5 ,7 etc .

λ = 4 L / n

for lowest frequency , wavelength will be highest . For highest  λ , n = 1

λ = 4 L = 4 x 5.99

= 23.96 m

frequency of wave = speed of wave / wavelength

= 2730 / 23.96 = 114 approx .

2 )

The frequency range heard by mouse = 1010 Hz to 90000 Hz .

The fundamental frequency ( lowest harmonic ) of flagpole is 114 Hz

Higher odd harmonics are also possible . If n be the lowest harmonic in the audible range of mouse ,

n x 114 = 1010

n = 8.85 or 9 th or 11 th

9 th is not in the option , 11 th is the right option .

d . 11 th is the answer .

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