# Frequency of Reflected Underwater Sound Wave

• betamu
In summary, the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling towards a ship at 4.95 m/s is 120 Hz. The frequency shift experienced by the whale is doubled when the waves are bounced off the whale and returned to the ship. This is due to the ship hearing the Doppler shifted frequency twice. It is important to note that in trying to solve the equation in one step, the frequency of the sound source was placed on the wrong side.
betamu

## Homework Statement

The sound source of a ship’s sonar system operates at
a frequency of 18.0 kHz. The speed of sound in water (assumed
to be at a uniform 20°C) is 1482 m/s. What is the difference
in frequency between the directly radiated waves and the waves
reflected from a whale traveling directly toward the ship at
4.95 m/s ? The ship is at rest in the water.

## Homework Equations

fship = (v+vship/v+vwhale)fwhale

## The Attempt at a Solution

To find the frequency of the reflected waves, I used the above equation with vship=0 and vwhale=-4.95m/s. Found the reflected frequency to be 18060.32Hz, which means a 60Hz difference. My textbook says it should be double that, 120Hz.

What you have determined is the frequency shift experienced by the whale if the whale were the receiver. Bouncing off the whale and returning to the ship doubles the effect. It’s as if the whale is now an emitter at the Doppler shifted frequency and the ship hears that frequency Doppler shifted again

By the way, I think in trying to do it in one step you’ve put f0 on the wrong side of the equation

CWatters
Step 1: Whale is listener and listener is moving
Step 2: Whale is source and source is moving.

## 1. What factors affect the frequency of reflected underwater sound waves?

The frequency of reflected underwater sound waves can be affected by several factors, including the depth of the water, the temperature and salinity of the water, and the composition of the seafloor or objects in the water.

## 2. How does the frequency of reflected underwater sound waves impact marine life?

The frequency of reflected underwater sound waves can have a significant impact on marine life. High frequency sounds can disrupt the communication and navigation of marine animals, while low frequency sounds can cause physical harm or behavioral changes in certain species.

## 3. Can the frequency of reflected underwater sound waves be measured?

Yes, the frequency of reflected underwater sound waves can be measured using specialized equipment such as hydrophones. These devices can detect and record the frequency, amplitude, and direction of sound waves in the water.

## 4. How does the frequency of reflected underwater sound waves affect underwater mapping and imaging?

The frequency of reflected underwater sound waves plays a crucial role in underwater mapping and imaging. Higher frequencies are better for creating detailed images, while lower frequencies can penetrate deeper into the water and provide broader coverage.

## 5. What is the relationship between the speed of sound and the frequency of reflected underwater sound waves?

The speed of sound in water is directly related to the frequency of reflected underwater sound waves. As the frequency increases, so does the speed of sound. This relationship is important for accurately measuring the distance and location of underwater objects using sound waves.

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