An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is termed to be higher by 100 Hz , than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is :

Question

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is termed to be higher by 100 Hz , than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is : (A)  200 Hz  (B)  150 Hz  (C)  100 Hz  (D)  250 Hz

Tardigrade Admin · Accepted Answer

An open pipe forms antinode at both ends. If length of pipe is l and v the velocity, then the fundamental frequency is given by

n = (v/2 l) Frequency of third harmonic of closed pipe is

n' = (3 v/4 l) Given, nÊ¹ â n = 100 ∴ (3 v/4 l) - (v/2 l) = 100 ⇒ (v/4 l) = 100 ⇒ (1/2)((v/2 l)) = 100 ∴ n = 200 Hz.

Q. An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is termed to be higher by $100 Hz$ , than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is :

$200 Hz$

$150 Hz$

$100 Hz$

$250 Hz$

Q. An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is termed to be higher by 100Hz , than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is :

200Hz

150Hz

100Hz

250Hz

An open pipe forms antinode at both ends. If length of pipe is l and v the velocity, then the fundamental frequency is given by n=2lv​ Frequency of third harmonic of closed pipe is n′=4l3v​ Given, nʹ−n=100 ∴4l3v​−2lv​=100 ⇒4lv​=100 ⇒21​(2lv​)=100 ∴n=200Hz.

Q. An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is termed to be higher by $100 Hz$ , than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is :

$200 Hz$

$150 Hz$

$100 Hz$

$250 Hz$