Question

A simplified model of a submarine sonar assumes that all objects echoing the signal are moving either straight toward or straight away from the detector. What is direction and magnitude of the velocity of a whale if a detector receives a signal of 26,730 Hz while the emitted signal had a frequency of 27,200 Hz. Consider the speed of sound in water vw = 1,500 m/s.

Select one:

a. whale moves toward detector with a velocity of 10.8 m/s

b. whale moves toward detector with a velocity of 13.1 m/s

c. whale moves away from the detector with a velocity of 10.8 m/s

d. whale moves away from the detector with a velocity of 13.1 m/s

Answer 1

speed of sound in water Us= 1500 m/s Actual frequency f= 27200 H2 Recieved frequency f' =26730 As the recieved frequency is less than actual frequency so whale is moving away from detector suppose speed of whale= there f' xf Ustu so usou Usto tead us- f'- 0.9827 f* Us-= 0.9827 G +0.9827 so 1.9820 = 0.0172 Us W = 0.0172 Us 9,982 0.0172 x 15 = 13.1 m/s 1.982 so option d)- whall moving away from detector with welocity 13 lm/s.