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 - Physics

Sum

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.

Solution

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 : $f = \frac{340}{2 \times 2 \times {10}^{- 2}} = 3 . 4 \text { kHz }$

(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 =$\frac{20, 000}{3400} = 5 . 8 = 5$

Concept: Speed of Wave Motion
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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 16 Sound Waves
Q 45 | Page 355