Dolphins of the open ocean are classified as Type II Odontocetes (toothed whales). These animals use ultrasonic "clicks" with a frequency of about 54.9 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 66 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.)
b. What is the wavelength of 54.9 kHz sound in the ocean?
a. To determine how much time elapses before the dolphin hears the echoes, we can use the formula:
Time = Distance / Speed
In this case, the distance is twice the depth of the ocean (because the sound has to travel down and back up), so the distance is 2 * 66 m = 132 m.
The speed of sound in seawater is given as 1530 m/s.
Using the formula, we can calculate the time as follows:
Time = 132 m / 1530 m/s = 0.0863 seconds (rounded to four decimal places)
Therefore, it takes approximately 0.0863 seconds for the dolphin to hear the echoes of the clicks.
b. To find the wavelength of the 54.9 kHz sound in the ocean, we can use the formula:
Wavelength = Speed / Frequency
The speed of sound in seawater is 1530 m/s, and the frequency is given as 54.9 kHz, which is equivalent to 54,900 Hz.
Converting the frequency to Hz, we can calculate the wavelength as follows:
Wavelength = 1530 m/s / 54,900 Hz = 0.0279 meters or 27.9 mm (rounded to four decimal places)
Therefore, the wavelength of the 54.9 kHz sound in the ocean is approximately 0.0279 meters or 27.9 mm.