Question

Help !!

You are using sonar over a spot in the ocean known to be 91.8 m deep. The system emits a 50.0-kHz pulse into the water. It takes 120.0 ms for the sound to travel to the ocean floor and back to the sonar system. Determine the speed of sound in the ocean and the wavelength of the sonar pulse.

Answer 1

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.