Question

A stationary sub uses sonar to send a 1.18x10^3 hertz sound wave through ocean water. The reflected sound wave from the flat ocean bottom is 324 meters below the sub is detected 0.425 seconds after it was sent from the submarine. Calculate the speed, v, wavelength and period of the sound wave

Answer 1

a) v = 1524.7 m/s

b) T = 8.47*10^-4 s

λ = 1.29 m

Step-by-step explanation:

a) First, in order to calculate the speed of the sound wave, you take into account that the velocity is constant, then, you use the following formula:

`v=(d)/(t)`

d: distance traveled by the sound wave, which is twice the distance to the ocean bottom = 2*324 m = 648 m

t: time that sound wave takes to return to the sub = 0.425

`v=(648m)/(0.425s)=1524.7(m)/(s)`

hence, the speed of the sound wave is 1524.7 m/s

b) Next, with the value of the velocity of the wave you can calculate the wavelength of the wave, by using the following formula:

`v=\lambda f\\\\\lambda=(v)/(f)`

f: frequency = 1.18*10^3 Hz

`\lambda=(1524.7m/s)/(1.18*10^3s^(-1))=1.29m`

And the period is:

`T=(1)/(f)=(1)/(1.18*10^3s^(-1))=8.47*10^(-4)s`

hence, the wavelength and period of the sound wave is, respectively, 1.29m and 8.47*10^-4 s