Question

Dolphins of the open ocean are classified as Type II Odontocetes (toothed whales). These animals use ultrasonic "clicks" with a frequency of about 55.3 kHz to navigate and find prey.
(A) Suppose a dolphin sends out a series of high-pitched clicks that are reflected back from the bottom of the ocean 86 m below. How much time elapses before the dolphin hears the echoes of the clicks? (The speed of sound in seawater is approximately 1530 m/s.)
answer in seconds
(B) What is the wavelength of 55.3 kHz sound in the ocean?
answer in mm

Answer 1

Answer:

Part a)

$\Delta t = 0.112 s$

Part b)

$\lambda = 27.7 mm$

Explanation:

Part a)

As we know that the sound will go to the bottom of the sea and then come back to the dolphin

so here total distance moved by the whale is given as

$d = 86 + 86$

$d = 172 m[tex]now the time to reach the sound back to initial position is given as[tex]\Delta t = \frac{d}{v}$

$\Delta t = \frac{172}{1530}$

$\Delta t = 0.112 s$

Part b)

As we know that frequency and wavelength are related to the speed of the wave as

$v = \lambda f$

$1530 = \lambda (55.3 \times 10^3)$

$\lambda = 0.0277 m$

$\lambda = 27.7 mm$