Question

The first two lengths of an air column in a resonance column method to measure speed of sound in air were found to be $50\text{cm}$ and $152\text{cm}$ respectively. If the velocity of sound in the laboratory is $340\text{m/s}$ . Find the frequency of the vibrating tuning fork and the end correction of the tube.

• A. $160\text{Hz},2\text{cm}$
• B. $160\text{Hz},1\text{cm}$
• C. $167\text{Hz},2\text{cm}$
• D. $167\text{Hz},1\text{cm}$

Answer 1

The correct option is D $167\text{Hz},1\text{cm}$

Given:
Length of first resonance $\left(l_1\right)=50\text{cm}$
Length of second resonance $\left(l_2\right)=152\text{cm}$

From formula of end correction $\left(e\right)$,

$e=\frac{l_2-3l_1}{2}$

Substituting the given data,

$e=\frac{152-3\times 50}{2}=1\text{cm}$

Also, from resonance column method, we know that

$\lambda =2(l_2-l_1)$

$\Rightarrow f=\frac{v}{2(l_2-l_1)}=\frac{340}{2(152-50)\times {10}^{-2}}\approx 167\text{Hz}$

Thus, option (d) is the correct answer.