Question

a pipe closed at one end has a length of 100 mm if the velocity of sound in the air of the pipe is 340m/s ,calculate
a)The fundamental

b)The first overtone

Answer 1

Given :

• Pipe is closed at one end ( i.e., it's closed organ pipe ) and its lenght is $\ell$ = 100mm or ${\sf 10^{-1}\:m}$
• Velocity of sound in air (v) = 340m/s

To Find :

• Fundamental frequency
• First overtone

Formula Used :

Fundamental Frequency or first harmonic

$\bullet\underline{\boxed{\sf f_1=\dfrac{v}{4\ell}}}$

v = speed of sound in the tube

First overtone or the third harmonic

$\bullet\underline{\boxed{\sf f_3=3f_1}}$

Solution :

a) Fundamental frequency

$\implies{\sf f_1=\dfrac{340}{4 \times 10^{-1}}}$

$\implies{\sf f_1=\dfrac{3400}{4} }$

$\implies{\bf f_1=850\: Hz}$

b)First overtone

$\implies{\sf f_3 = 3 \times 850 }$

$\implies{\bf_3=2550 \; Hz}$

Answer :

a) Fundamental frequency 850 Hz

b) First overtone 2550 Hz