Question

On vibrating an air column at ${27}^o$C and a tuning fork simultaneously, $5$ beats per second are produced. The frequency of the fork is less than that of air column. No beats are heard at $-3^o$C. The frequency of the fork is ___

• A. 70 Hz
• B. 147 Hz
• C. 104 Hz
• D. 95 Hz

Answer 1

Answer: (D)

95 Hz

frequency of air column = $k\times v$

and $\frac{v_{T2}}{v_{T1}}=\sqrt{\frac{T}{T_0}}$ (relation between speed and temperature)

let frequency of tuning fork is $f_0$

frequency of air column at $300K=k\times v_{300k}=f_1$

frequency of air column at $270K=k\times v_{270k}=f_2$

applying relation between speed and temperature , we have

$\frac{v_{270K}}{v_{300K}}=\sqrt{\frac{270}{300}}=0.95$

$f_2=0.95\times f_1$

on decreasing temperature the frequency of air column decreases and as per question beats are decreasing so air column was having higher frequency at $300K$ and difference in frequency of air column at $300K$ and fork is equal to no of beats and frequency of air column at $270K$ is equal to frequency of fork. so

$0.05\times f_1=5$

$f_1=100$

frequency of fork = $100-5=95$