CONCEPTUAL=PHY1 A class destroyer is scouting the North Atlantic for a rogue sub

Question

CONCEPTUAL=PHY1

A class destroyer is scouting the North Atlantic for a rogue submarine operated by terrorists. It has a towed sonar array that works at a frequency of 100 kHz to paint the surrounding depths with sound waves in water. The terrorists have an older model sonar which operates at 10 kHz. If each ship emits sound waves for an instant directly toward each other (a "ping"), then who observes the reflection first, and why? You may ignore changes in depth. How do the wavelengths of the sound waves compare?

Explanation / Answer

sice speed of sound wave is constant, both wave travell with same speed and hence both will observe the reflection at the first time.

speed of sound is 340 m/s
for 100 khz,
wavelength = speed/frequency
= 340 / (100*10^3 Hz)
= 3.4*10^-3 m

for 10 khz,
wavelength = speed/frequency
= 340 / (10*10^3 Hz)
= 3.4*10^-2 m

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