Question

A submarine moving at 20knots emits a sound wave from its sonar and got a ping from a giant moving squid that is also moving towards the submarine but at 24knots. The frequency generated by the sonar is ƒs=20,000kHz. The density of sea water is 1027kg/m^3 and the bulk modulus is Bs=2.34GPa. Find the frequency shift in the reflected wave detected by the sonar.

hint: You need to split the problem into two parts. Part 1 is finding the frequency heard by the squid. Part 2 is using the shifted frequency found in Part 1 as the source frequency for the reflected wave coming from the squid. Use the Doppler shift formula to find the received frequency detected by the submarine sonar.

Answer 1

we know,

1 knot = 0.514444 m/s

so,

v_submarine = 20 knots

= 20*0.51444

= 10.29 m/s

v_squid = 24 knots

= 24*0.51444

= 12.34 m/s

given

B = 2.34 Gpa = 2.34*10^9 Pa

rho = 1027 kg/m^3

speed of sound in water, v_sound = sqrt(B/rho)

= sqrt(2.34*10^9/1027)

= 1509 m/s

frequency observed by the squid,

f' = fs*(v_sound + v_squid)/(v_sound - v_submarine)

= 20000*(1509 + 12.34)/(1509 - 10.29)

= 20302 kHz

frequency received detected by the submarine sonar

f'' = f'*(v_sound + v_submarine)/(v_sound - v_squid)

= 20302*(1509 + 10.29)/(1509 - 12.34)

= 20609 kHz <<<<<<<<<------------Answer