Final answer:
The speed of sound in the ocean is calculated to be 1530 m/s based on the given time for the sonar to return. The wavelength of the sonar pulse is found to be 3.06 cm using the sound's speed and frequency.
Step-by-step explanation:
To determine the speed of sound in the ocean and the wavelength of the sonar pulse, we need to use the information given: a 50.0 kHz pulse is emitted and takes 120.0 ms to travel to the ocean floor and back.
First, let's find the speed of sound in the ocean. The sound travels a distance of 2 x depth (down and back up). Therefore, the total distance is 2 x 91.8 m = 183.6 m. The time taken is 120.0 ms or 0.120 s. Using the formula speed = distance / time, the speed of sound is:
Speed = 183.6 m / 0.120 s = 1530 m/s.
Now, to find the wavelength (λ), we use the formula λ = speed / frequency. With the frequency (f) given as 50.0 kHz or 50,000 Hz, the calculation is:
Wavelength = 1530 m/s / 50,000 Hz = 0.0306 m or 3.06 cm.
Therefore, the speed of sound in the ocean is 1530 m/s, and the wavelength of the sonar pulse is 3.06 cm.