Question

A source of frequency 10 kHz when vibrated over the mouth of a closed organ pipe is in unison at 300 K. The beats produced when temperature rises by 1 K is

• A. 30 Hz
• B. 13.33 Hz
• C. 16.67 Hz
• D. 40 Hz

Answer 1

The correct option is C 16.67 Hz

$n_1\propto \sqrt{T}{n}_2\propto \sqrt{T^{\prime }}$
$\frac{n_1}{n_2}=\sqrt{\frac{T}{T^{\prime }}}=\sqrt{\frac{300}{301}}$
$\frac{n_1}{n_2}={(1+\frac{1}{300})}^{\frac{1}{2}}=1+\frac{1}{600}$
$n_2=n_1+\frac{10000}{600}$
$n_2-n_1=16.67Hz$