A pipe 0.20m long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source ? Will the same source be resonance with the pipe if both ends are open ? ( Speed of sound in air is `340 ms^(-1)` )

Explanation

Given, `L = 0.20m` ( closed pipe ) , `f = 430 Hz. V = 340 ms^(-1)`
For a closed pipe system, fundamental frequency ( I harmonic ) `f = ( v )/( lambda)`
where `L = ( lambda )/(4)`, Hence `f = ( V )/( 4L)`
i.e., `f = ( 340)/( 4 xx 0.2) = 425 Hz`
Since the fundamental frequency is nearly equal to the given source, the I harmonic will resonate with it.
For Open pipe system,` f = ( v )/( 2L ) ( 340)/( 2 xx 0.2)= 850 Hz`
Hcen the given source does not vibrate with the open pipe system.