A ship mapping the depth of the ocean emits a sound of 37 kHz. The sound travels to the ocean floor and returns 0.65 s later.
(a) How deep is the water at that location?
m
(b) What is the wavelength of the wave in water?
cm
(c) What is the wavelength of the reflected wave as it travels into the air, where the speed of sound is 350 m/s?
mm
Someone please help me one this please! I have no clue how to do it; thank you.
To find the depth of the water, we can use the formula for the speed of sound in water, which is given by:
Speed = Distance / Time
In this case, the speed of sound in water is not provided, but we can calculate it using the given information.
(a) Calculating the depth of the water:
1. Determine the speed of sound in water:
We know that the speed of sound in air is approximately 343 m/s (at 20 degrees Celsius). However, the speed of sound in water is much higher, around 1500 m/s, so we will use this value instead.
2. Calculate the round trip distance traveled by the sound wave:
Since the sound wave travels from the ship to the ocean floor and then back to the ship, we need to consider the distance traveled in both directions. The formula to calculate the round trip distance is:
Round Trip Distance = 2 * Depth
3. Calculate the round trip time:
The time taken by the sound wave to travel down to the ocean floor and back to the ship is given as 0.65 s.
4. Use the formula to find the depth of the water:
By rearranging the speed equation, we can solve for the depth:
Depth = (Speed * Time) / 2
Substituting the known values, we get:
Depth = (1500 m/s * 0.65 s) / 2
Calculating this expression will give you the depth in meters.
(b) Calculating the wavelength of the wave in water:
The formula to calculate the wavelength is:
Wavelength = Speed / Frequency
We know the frequency of the wave emitted by the ship mapping the ocean floor is 37 kHz, which is equivalent to 37,000 Hz.
Substituting the known values, we get:
Wavelength = (Speed of sound in water) / (37,000 Hz)
Calculating this expression will give you the wavelength in meters.
(c) Calculating the wavelength of the reflected wave in the air:
We can use the formula:
Wavelength (in air) = (Speed of sound in air) / Frequency
Given that the speed of sound in air is 350 m/s and the frequency is the same as in part (b) (37 kHz or 37,000 Hz), the formula becomes:
Wavelength (in air) = 350 m/s / 37,000 Hz
Calculating this expression will give you the wavelength in meters.