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
Please help; I don't know how to do this someone please help. Thank you.
To solve this problem, we will use the equation of motion for sound:
Distance = Speed × Time
(a) To find the depth of the water, we need to find the distance traveled by the sound wave. The sound wave travels from the ship to the ocean floor and then back to the ship. Since the sound wave travels the same distance twice, we can divide the total distance traveled by 2 to find the depth of the water.
First, let's find the total distance traveled by the sound wave:
Total distance traveled = Speed × Time
The speed of sound in water is approximately 1500 m/s (since the question does not provide the speed, we will assume an average value).
Total distance traveled = 1500 m/s × 0.65 s
Now, let's divide the total distance traveled by 2 to find the depth of the water:
Depth of water = (1500 m/s × 0.65 s) / 2
Calculating this expression will give us the depth of the water in meters.
(b) To find the wavelength of the wave in water, we need to use the formula:
Wavelength = Speed / Frequency
The speed of sound in water is 1500 m/s (as assumed above). The frequency of the sound emitted by the ship is 37 kHz, which can be converted to Hz by multiplying it by 1000.
Wavelength (in meters) = 1500 m/s / (37 kHz × 1000 Hz)
Calculating this expression will give us the wavelength of the wave in meters. To convert the wavelength into centimeters, multiply the result by 100.
Wavelength (in cm) = (Wavelength in meters) × 100
(c) Finally, to find the wavelength of the reflected wave as it travels into the air, we need to use the formula:
Wavelength = Speed / Frequency
The speed of sound in air is 350 m/s.
Wavelength (in meters) = 350 m/s / (37 kHz × 1000 Hz)
Calculating this expression will give us the wavelength of the reflected wave in meters. To convert the wavelength into millimeters, multiply the result by 1000.
Wavelength (in mm) = (Wavelength in meters) × 1000
Now you can solve each part of the problem step-by-step using the formulas and calculations provided.
To solve these questions, we need to use the formula for the speed of sound in a medium, which is given by:
Speed = Frequency x Wavelength
We also need to know some additional information about the speed of sound in water and air. The speed of sound in water is about 1,500 m/s, and in air, it is about 350 m/s.
(a) To find the depth of the water, we'll use the formula for the distance traveled by sound, given by:
Distance = Speed x Time
In this case, the sound wave travels to the ocean floor and back, so the total distance is twice the depth of the water. By rearranging the formula, we can solve for the depth:
Depth = (Speed x Time) / 2
Substituting the given values:
Depth = (1,500 m/s x 0.65 s) / 2
Solving this equation gives us the depth in meters.
(b) To find the wavelength of the wave in water, we can rearrange the speed formula:
Wavelength = Speed / Frequency
Substituting the given values:
Wavelength = 1,500 m/s / 37,000 Hz
Converting Hz to kHz:
Wavelength = 1,500 m/s / 37,000 kHz
The result will be in meters, but if we need the answer in centimeters, we can convert it by multiplying by 100.
(c) To find the wavelength of the reflected wave in the air, we can again use the speed formula:
Wavelength = Speed / Frequency
Substituting the given values:
Wavelength = 350 m/s / 37,000 Hz
Converting Hz to kHz:
Wavelength = 350 m/s / 37,000 kHz
The result will be in meters, but if we need the answer in millimeters, we can convert it by multiplying by 1,000.
I hope this helps! Let me know if you have any further questions.