A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency ν. The value of ν is close to:

(Speed of sound in water = 1500 m/s)

Concept:

Doppler Effect states that frequency change and wavelength wave can observe by the relative source.

Where, C is the wave velocity

λ wavelength

T is the time

Doppler Effect, the relationship between the emitted frequency is given by the formula:

Calculation:

The position of the submarine A and B is given in the image below:

The velocity of submarine A is:

The velocity of submarine B is:

From the question, we can understand that Doppler Effect is taking place between two submarines.

According to Doppler Effect, the relationship between received and emitted frequency is given by the formula:

Where,

f = Observed frequency

f₀ = Emitted frequency

c = Velocity of waves in the medium

v_r is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction)

v_s is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction)

From question, we need to find the frequency of A.

The Frequency of A is given by the formula:

Where,

f_A = Frequency of A (observed frequency)

f_B = Frequency of B (emitted frequency) = 500 Hz (given)

V = Velocity of water = 1500 m/s (given)

The Frequency of B is given by the formula:

Now, substituting frequency of A,

⇒ f_B = [1.00166][1.00167](500)

∴ f_B = 501.66 Hz ≈ 502 Hz