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

Question

Physics

Tara Coffey

21 January, 06:00

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

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Krista Eaton · Answer 1

B) 1.5 m/s

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