Question

A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ________ m/s.

Answer 1

For a closed pipe of length $L = 150 \, \text{cm} = 1.5 \, \text{m}$:

The fundamental frequency is given by:

$f_c = \frac{v}{4L}.$

For an open pipe of length $L = 350 \, \text{cm} = 3.5 \, \text{m}$:

The fundamental frequency is given by:

$f_o = \frac{v}{2L}.$

Given that the beat frequency is:

$|f_c - f_o| = 7 \, \text{Hz}.$

Substituting:

$\left| \frac{v}{4 \cdot 1.5} - \frac{v}{2 \cdot 3.5} \right| = 7.$

Simplifying:

$\left| \frac{v}{6} - \frac{v}{7} \right| = 7.$

Solving for $v$:

$\frac{v}{42} = 7 \implies v = 42 \cdot 7 = 294 \, \text{m/s}.$

The Correct answer is: 294