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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.

Sagot :

Answer:

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 .

snehashish65

1. The lowest frequency standing wave that can be formed on the flagpole is 114 Hz.

2.  The lowest flagpole harmonic that the mouse can hear is 11th. Hence, option (d) is correct.

What is the frequency of the sound wave?

When a sound wave is propagating through any medium, such that the total wave produced in one second, is known as the frequency of the sound wave.

1.

Given data:

The height of fiberglass is, h = 5.99 m.

The wave propagation speed in fiberglass is, v = 2730 m/s.

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

n x λ / 4 = L

here,

L is the length of the pole.

n is an odd integer like 1, 3, 5,7, etc.

Arranging the above expression as,

λ = 4 L / n

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

λ = 4 L

λ = 4 x 5.99

λ = 23.96 m

frequency of wave = speed of wave / wavelength

frequency of wave = 2730 / 23.96

frequency of wave = 114 Hz

Thus, we can conclude that the lowest frequency standing wave that can be formed on the flagpole is 114 Hz.

2.

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

The fundamental frequency ( lowest harmonic ) of the 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

Thus, we can conclude that the lowest flagpole harmonic that the mouse can hear is 11th. Hence, option (d) is correct.

Learn more about standing wave frequency here:

https://brainly.com/question/1967686

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