A research vessel uses an ultrasonic SONAR system that emits pulses of frequency 30kHz into seawater. An echo from the ocean floor is received 1.2s after the pulse is transmitted. The speed of sound in seawater is 1500m/s.
(i) Derive an expression for the depth d of the ocean floor in terms of the speed of sound v in water and the total time interval t between emission and reception of the echo.
(ii) Using your expression, calculate the depth of the ocean at the point directly below the vessel.
(iii) Determine the wavelength of the 30kHz ultrasonic wave in seawater.
(iv) How many complete wavelengths does the pulse cover in making the round trip from the ship to the ocean floor and back? Show your working clearly.
(v) The same transmitter is tested in air where the speed of sound is 340m/s. Predict the wavelength of the 30kHz sound in air and compare it with the wavelength in seawater.