Question

In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter $5\text{cm}$ is used. The air column in the pipe resonates with a tuning fork of frequency $500\text{Hz}$ , when the minimum length of the air column is $15.5\text{cm}$. Find the speed of sound in air at room temperature.

• A. $330\text{m/s}$
• B. $335\text{m/s}$
• C. $340\text{m/s}$
• D. $345\text{m/s}$

Answer 1

The correct option is C $340\text{m/s}$

Given,
Diameter of pipe $\left(d\right)=5\text{cm}\text{or}0.05\text{m}$

Minimum length of air column $\left(l_{min}\right)=15.5\text{cm}\text{or}0.155\text{m}$

Frequency of tuning fork $\left(f\right)=500\text{Hz}$

Let ${}^{\prime }{e}^{\prime }$ be the end correction which is equal to $0.3d$.

We know that,

Fundamental frequency of closed pipe of length $l$ is given by

$f=\frac{v}{4(l+e)}=\frac{v}{4(l+0.3d)}$

Substituting the given data,

$500=\frac{v}{4\left[\right(0.155)+(0.3\times 0.05\left)\right]}\Rightarrow v=340\text{m/s}$