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? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-15 Waves



Q.17:- 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:-

First (Fundamental); No
Length of the pipe, l = 20 cm = 0.2 m
Source frequency = nth normal mode of frequency, νn = 430 Hz
Speed of sound, v = 340 m/s
In a closed pipe, the nth 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 nth mode of vibration frequency is given by the relation:
vn = nv/2l
n = 2lvn/v