Question

A sonar generator on a submarine produces periodic ultrasonic waves at a frequency of 2.00 x 10^6 Hz. The wavelength of the waves in seawater is 7.50 x 10^-4 m. When the generator is directed downward, an echo reflected from the ocean floor is received 5.00 s later. Calculate the depth of the ocean at that point.

Answer 1

The first step is to find the velocity of generated wave. The formula for finding velocity is expressed as

velocity = frequenccy x wavelength

From the information given,

frequency = 2.00 x 10^6 Hz.

wavelength = 7.50 x 10^-4 m.

Velocity = 2.00 x 10^6 x 7.50 x 10^-4 m = 1500 m/s

When the echo is heard, the distance travelled is 2d(the sound travels back and forth when the echo is heard)

Recall,

distance = velocity x time

In this case,

distance = (velocity x time)/2

time after the echo travelled a distance of 2d = 5 seconds

Distance = (1500 x 5)/2 = 3750

The depth of the ocean is 3750 m