Question

An open organ pipe has a length of 5 cm. (a) Find the fundamental frequency of vibration of this pipe. (b) What is the highest harmonic of such a tube that is in the audible range? Speed of sound in air is 340 m s⁻¹ and the audible range is 20-20,000 Hz.

Answer 1

Given:
Length of organ pipe ^_$L$ = 5 cm = 5 × 10⁻² m
v = 340 m/s
The audible range is from 20 Hz to 20,000 Hz.
The fundamental frequency of an open organ pipe is:
$f=\frac{v}{2L}$
On substituting the respective values ,we get:
$f=\frac{340}{2\times 2\times {10}^{-2}}=3.4\mathrm{kHz}$

(b) If the fundamental frequency is 3.4 kHz, then the highest harmonic in the audible range (20 Hz - 20 kHz) is

Required highest harmonic = $\frac{20,000}{3400}=5.8=5$