Find the frequency of fifth overtone of an air column vibrating in a pipe closed at one end. Length of pipe is 42.10 cm long and speed of sound in air at room temperature is 350 m/s. (Inner diameter of pipe is 3.5 cm)
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Given :
l = 42.10cm
= 42.10 × 10⁻² m
= 0.4210 m
v = 350 m/s
d = 3.5 cm = 3.5 × 10⁻² m
= 0.035 m
Fundamental frequency in air column closed at one end is given by
n = V /4L
N=[350/4x 0.4315]
N=350/4x0.4315
N=202.78Hz
Pth overtone is given by np=(2p+1)n
Frequency of fifth overtone is
N5=(2x5+1)n
N5=11n
=11x202.78
=2230.59Hz
∴ the frequency of fifth overtone of an air column vibrating in a pipe closed at one end is 2230.59Hz
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Answer:
Given :
l = 42.10cm
= 42.10 × 10⁻² m
= 0.4210 m
v = 350 m/s
d = 3.5 cm = 3.5 × 10⁻² m
= 0.035 m
Fundamental frequency in air column closed at one end is given by
n = V /4L
N=[350/4x 0.4315]
N=350/4x0.4315
N=202.78Hz
Pth overtone is given by np=(2p+1)n
Frequency of fifth overtone is
N5=(2x5+1)n
N5=11n
=11x202.78
=2230.59Hz
∴ the frequency of fifth overtone of an air column vibrating in a pipe closed at one end is 2230.59Hz
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