Question

A tuning fork P of unknown frequency gives 7 beats in 2 seconds with another tuning fork Q. When Q runs towards a wall with a speed of 5 m/s it gives 5 beats per second with its echo. On loading P with wax, it gives 5 beats per second with Q. What is the frequency of P (in Hz)? Assume speed of sound = 332 m/s.

Answer 1

If $P,Q$ are frequencies then,

$P-Q=3.5Hz$

$Q^{\prime }=Q\left(\frac{v}{v-5}\right)$

$Q^{\prime }=Q=5(v=332m/s)$

$Q[\frac{v}{v-5}-1]=5$

$Q=327Hz$

$P=3.5+Q=330.5Hz$