A pipe 20 cm 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 in resonane with the pipe if both end are open ? (speed of sound in air is `340 m s^(-1))`.

Explanation

(1) For closed pipe, first harmonic is,
`f _(1) = (v)/(4L) = (340)/(4 xx 0.2) = 425 Hz`
`to f ~f _(1) (because =430 Hz)`
Difference `f- f _(1)= 430 - 425 =5 Hz ` is very small and so vibrations of soucrce will nearly produce resonance in the air column in the closed pipe.
(2) For an open pipe, first harmonic is,
`f._(1) = (v)/(2L) = (340)/(2 xx 0.2) =850Hz`
Other harmonics are `2f _(1), 3f _(1), 4f_(1),...` which are greater than 850 Hz. Here no frequency matches with frequency 430 Hz of source. Hence, given source can not produce resonance in an open pipe of length 20 cm.