Question

Two tuning forks when sounded together gives 9 beats in 3 second. One of the forks is in unison with 1 m long sonometer wire and the other with 1.02 m of the same wire, the tension being the same in the two cases. Then, the frequencies of the forks are (in Hz)

• A. 147,150
• B. 153,150
• C. 459,450
• D. 450,441

Answer 1

The correct option is B 153,150

$f_1=\frac{1}{2l_1}\sqrt{\frac{T}{m}}$
$f_2=\frac{1}{2l_2}\sqrt{\frac{T}{m}}$

Here $l_1=1.0m,l_2=1.02m$
$\frac{1}{2\times 1}\sqrt{\frac{T}{m}}-\frac{1}{2\times 1.02}\sqrt{\frac{T}{m}}=3Hz$
$\sqrt{\frac{T}{m}}\left(\frac{0.04}{2\times 2.04}\right)=3\Rightarrow \sqrt{\frac{T}{m}}=\frac{3\times 2\times 2.04}{0.04}=306$,
$f_1=\frac{1}{2}\sqrt{\frac{T}{m}}=153Hz$

$f_2=150Hz$
Option "B" is correct.