Question

From diagram given below calculate:

1. velocity of P and Q
2. frequency of P, when frequency of Q is 512 Hz.

Assume that both wave are traveling in same medium.

Answer 1

For Q:

Wavelength (λ) = Distance between two consecutive crests

= 0.5 - 0.1 = 0.4 m

Frequency(f) = 515 Hz

Velocity(v) = λf

= 0.4 × 512 = 204.8 ms^-1 

Since both waves are travelling in same medium and velocity of P and Q is same i.e. 204.8 ms^-1 

For P:

Wavelength = λ' = 1.0 - 0.2 = 0.8 m

Velocity = v = 204.8 ms^-1 

Frequnecy of wave P = f' = ?

v = λ'f'

f = ${\displaystyle \frac{\text{v}}{\lambda \prime }=\frac{204.8}{0.8}=256}$ Hz