Question

A pipe 20 cm long Is closed at one end. Which harmonic mode of the pipe 1s 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

Given : 

l = 20 cm = 0.2 m

v = 340 ms^-1

f = 430 Hz

For a pipe closed at one end :

f = \(\frac{(2n-1)v}{4l}\) n = 1, 2, 3 ……

⇒ 430 = (2n-1)\(\frac{340}{4 \times 0.2}\)

⇒ n = 1

⇒ Resonance occurs only for first/fundamental mode of vibration. For a pipe open at both ends,

f = nv/2l n = 1, 2, …..

⇒ 430 = \(\frac{n \times 340}{2 \times 0.2}\)

⇒ n = 0.51 

Since n<1, resonance does not occur.