Question

Two tuning forks A and B give 5 beats/s. A resonates with a column of air 15 cm long, closed at one end, and B with a column 30.5 long, open at both ends. Neglecting end correction, the frequencies of A and B are respectively

• A. 305, 295 Hz
• B. 295 Hz, 300 Hz
• C. 305 Hz, 300 Hz
• D. 300 Hz, 305 Hz

Answer 1

The correct option is C 305 Hz, 300 Hz

We have,

for $A:$

$\begin{array}{c}\frac{{\lambda }_A}{u}=\frac{15}{100}\\ \Rightarrow {\lambda }_A=\frac{60}{100}=\frac{V}{f_A}\\ \Rightarrow f_A=\frac{V\times 100}{60}\end{array}$

for $B:$

$\begin{array}{c}\frac{{\lambda }_B}{2}=\frac{30.5}{100}\\ \Rightarrow {\lambda }_B=\frac{61}{100}=\frac{V}{f_B}\\ \Rightarrow f_B=\frac{V\times 100}{61}\end{array}$

So that,

$A/C.$ $f_A-f_B=5$

$\begin{array}{c}\Rightarrow \frac{V\times 100}{60}-\frac{V\times 100}{61}=5\\ \Rightarrow V\times 100\left(\frac{1}{61\times 60}\right)=5\\ \Rightarrow V=183\end{array}$

$\therefore f_A=\frac{183\times 100}{60}=305$

and

$f_B=300$

Hence,

Option $C$ is correct answer.