An ultrasonic wave in water is a compression wave that travels at 1,400 m/s

A) An ultrasonic wave from a ship travels to the bottom of a lake and back in 0.16s. How deep is it at this point?

B) If an ultrasonic wave is emitted in the ocean where the ocean's depth is 3.5km, how long will the echo take to return?

Show all work

2 d = 1400 * .16

d = 112 meters deep

2 d = v t
2 * 1000 * 3.5 = 1400 t
t = 5 seconds

A) To determine the depth of the lake, we can use the formula:

Depth = (Speed of the ultrasonic wave * Time taken) / 2

Given:
Speed of the ultrasonic wave in water = 1,400 m/s
Time taken = 0.16 s

Using these values in the formula, we get:

Depth = (1,400 m/s * 0.16 s) / 2
Depth = 224 m

Therefore, the depth of the lake at this point is 224 meters.

B) To calculate the time it takes for the ultrasonic wave to travel to the ocean floor and back, we can use the same formula:

Time taken = (2 * Depth) / Speed of the ultrasonic wave

Given:
Depth of the ocean = 3.5 km = 3,500 m
Speed of the ultrasonic wave in water = 1,400 m/s

Using these values in the formula, we get:

Time taken = (2 * 3,500 m) / 1,400 m/s
Time taken = 7,000 m / 1,400 m/s
Time taken = 5 s

Therefore, the ultrasonic wave will take 5 seconds to travel to the ocean floor and back.