Question

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 v. The value of v is close to :
(Speed of sound in water = 1500 ms⁻¹)
(A) 499 Hz (B) 502 Hz
(C) 504 Hz (D) 507 Hz

Answer 1

Given:

• Speed of sound in water $(v) = 1500 ms^{-1}$
• $f_0 = 500Hz$
• Speed of sub marine $(A) = v_a = 18 km/hr$
• Speed of sub marine $(B) = v_b = 27 km/hr$

To Find:

• Frequency received by B

Solution:

frequency received by $A = f'$

            $f'= (\frac{v-v_a}{v-v_b})f_0$

$v_a = 18 km/hr = 5m/s$

$v_b = 27 km/hr = 7.5 m/s$

            $f'= (\frac{1500-5}{1500-7.5})500$

frequency received by $B = f''$

          $f''= (\frac{v+v_b}{v+v_a})f'$

         $f''= (\frac{1500+7.5}{1500+5}) (\frac{1500-5}{1500-7.5}) 500$

           $f'' = 502Hz$

Thus, frequency received by$B = f'' = 502Hz$