Question

A tuning fork and an air column whose temperature is $51^{\circ }C$ produce $4$ beats in one second, when sounded together. When the temperature of air column decreases the number of beats per second decreases. When the temperature remains $16^{\circ }C$ only one beat per second is produced. The frequency of the tuning fork is

• A. 100 Hz
• B. 75 Hz
• C. 150 Hz
• D. 50 Hz

Answer 1

Answer: (D)

$\frac{F+4}{F+1}=\sqrt{\frac{273+51}{273+16}}$
$\frac{f+4}{f+1}-\sqrt{\frac{324}{289}}$
$\frac{f+4}{f+1}=\frac{18}{17}$
$f=50Hz$