Answer
(a) The depth of the water is $521~m$
(b) $\lambda = 4.0~cm$
(c) $\lambda = 9.2~mm$
Work Step by Step
(a) We can use $v = 1533~m/s$ as the speed of sound in the water. We can find the total distance the sound traveled in the water:
$d = v~t = (1533~m/s)(0.68~s) = 1042~m$
Since the sound reached the bottom and returned to the ship, the depth of the water is $\frac{1042~m}{2} = 521~m$
(b) We can find the wavelength of the wave in the water:
$\lambda = \frac{v}{f}$
$\lambda = \frac{1533~m/s}{38,000~Hz}$
$\lambda = 0.040~m$
$\lambda = 4.0~cm$
(c) When a wave moves from one medium into another medium, the frequency does not change. We can find the wavelength of the wave in the air:
$\lambda = \frac{v}{f}$
$\lambda = \frac{350~m/s}{38,000~Hz}$
$\lambda = 0.0092~m$
$\lambda = 9.2~mm$
