A pipe of 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a `2.2` kHz source? Given, speed of sound in

Question

A pipe of 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a `2.2` kHz source? Given, speed of sound in

A pipe of 60 cm long and open at both the ends
produces harmonics. Which harmonic mode of pipe
resonates a `2.2` kHz source? Given, speed of sound in
ari ` = 300 ms^(-1)`.
A. Fifth harmonic
B. Eighth harmonic
C. Third harmonic
D. Second harmonic

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - b
According to the modes of vibration of air column in
open organ pipe.
First mode of vibration `v_(1)=v/(2l)`
The frequency of nth mode of vibration
`v_(n)=nxxv_(1)=nxx(v/(2l))`
Given, `v_(n)=2.2 kHz = 2200 Hz, v= 330 ms^(-1)`
`l= 60 cm = 0.60 m`
`n= (2200xx 2xx 0.60)/330=2640/330=8`
So, eighth harmonic mode of pipe resonates.