Question

On vibrating an air column at ${627}^{\circ }C$ and a tuning fork simultaneously, $6$ beats/sec are heard. The frequency of fork is less than that of air column. No beats are heard at $-{48}^{\circ }C$. the frequency of fork is:-

• A. $3Hz$
• B. $6Hz$
• C. $10Hz$
• D. $15Hz$

Answer 1

Answer: (B)

$6Hz$

The frequency of the air column will be $n+6$ at ${627}^{0}C$ and $nat-{48}^{0}C$

Using velocity- frequency relation

$v=n\lambda$

$v_{627}=(n+6)\lambda$

$v_{-48}=n\lambda$

So, $\frac{v_{627}}{v_{-48}}=\frac{(n+6)\lambda }{n\lambda }=1+\frac{6}{n}$. . . . . .(1)

The speed of sound is directly proportional to the square root of the absolute temperature

$\frac{v_{627}}{v_{-48}}=\sqrt{\frac{627+273}{-48+273}}=\sqrt{\frac{900}{225}}=2$

From equation (1), we get

$1+6/n=2$

$n=6Hz$

The correct option is B.