Question

In the figure, a French submarine and a U.S. submarine move toward each other during maneuvers in motionless water in the North Atlantic. The French sub moves at speed v_F = 47.00 km/h, and the U.S. sub at v_US = 73.00 km/h. The French sub sends out a sonar signal (sound wave in water) at 1.000 × 10³ Hz. Sonar waves travel at 5470 km/h. (a) What is the signal’s frequency as detected by the U.S. sub? (b) What frequency is detected by the French sub in the signal reflected back to it by the U.S. sub?

Answer 1

Let,

• : be the speed of sonar waves.
•    : be the original frequency of the sonar wave
• : be the frequency detected by the U.S. submarine
•     : be the frequency detected by the French submarine.

Given:-

• 
• 
• 
• 

In this problem, we will use Doppler effect in sound to obtain the frequencies detected by the submarines. According to the Doppler effect the frequency detected by the observer is different than the original one if there is relative motion between the source and observer. If source and observer are moving toward each other, then the apparent frequency heard by the observer is given by,

(a) What is the signal’s frequency as detected by the U.S. sub? :

In this case, the French submarine is source and US submarine is observer. Since both submarines moving toward each other, according to Doppler effect, the frequency detected by the US submarine is given as,

By plugging all the known values in above equation we get,

or

This is the signal’s frequency as detected by the U.S. submarine.

(b) What frequency is detected by the French sub in the signal reflected back to it by the U.S. sub? :-

In this case the signal reflected from the US submarine, and therefore the US submarine becomes the source and French submarine becomes observer. Both submarines i.e. source and observer are moving toward each other. The signal's frequency that reflected from US submarine will acts as the original frequency. Therefore, from Doppler effect we can have,

By plugging all the known values in the above equation we get,

or

This is the frequency detected by the French submarine in the signal reflected back to it by the U.S. submarine.