Question

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 resonance with the pipe if both ends are open? (Speed of sound in air is 340 m s^–1 ).

Answer 1

First (Fundamental); No

Length of the pipe, l = 20 cm = 0.2 m

Source frequency = n^th normal mode of frequency, ν_n = 430 Hz

Speed of sound, v = 340 m/s

In a closed pipe, the n th normal mode of frequency is given by the relation:

Hence, the first mode of vibration frequency is resonantly excited by the given source. 

In a pipe open at both ends, the n^th mode of vibration frequency is given by the relation: 

Since the number of the mode of vibration (n) has to be an integer, the given source does not produce a resonant vibration in an open pipe.