Question

A submarine can detect an approaching enemy submarine using sonar. If a stationary submerged submarine emits a 100kHz tone and receives a tone Doppler shifted by 200Hz, calculate the speed of the enemy submarine if the speed of sound in salt water is 1,482m/s. Note: Because the echo is off of a moving object, the moving object amplifies the Doppler effect by a factor of 2! Therefore, the speed must be cut in half. A. 1.0m/s B. 1.5m/s C.2.2m/s OD.3.3m/s E. 4.4m/s

Answer 1

B) 1.5 m/s

Step-by-step explanation:

The apparent frequency will be enhanced due to Doppler effect

If f be the apparent frequency , F be the real frequency , V be the velocity of sound and v be the velocity of approaching submarine then f is given by

f = F \frac{V+v}{V-v}\\

\frac{f}{F} =\frac{V+v}{V-v}\\

\frac{f}{F}-1 =\frac{V+v}{V-v}-1\\

\Delta f = \frac{2vf}{V-v}\\

200=\frac{2\times v\times 100\times 1000}{1482-v}\\

v=1.48 m/s