How Does the Doppler Effect Calculate Submarine Depth and Velocity?

In summary, a destroyer with sonar sends out pulses of sound at 30.000 MHz and receives reflected pulses from a submarine directly below with a 60 ms time delay at a frequency of 29.958 MHz. Using the speed of sound in seawater at 1.55 km/s, the depth of the submarine can be calculated to be 93m. To find the vertical velocity of the submarine, the equation v=lambda*f is used, where lambda is the wavelength and f is the frequency. By assigning values of v=1550 m/s, u_s=0 m/s, f_s=29.958E6 Hz, and f=30E6 Hz, the vertical velocity is calculated to be 1,
  • #1
krtica
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A stationary destroyer is equipped with sonar that sends out pulses of sound at 30.000 MHz. Reflected pulses are received from a submarine directly below with a time delay of 60 ms at a frequency of 29.958 MHz.
(a) If the speed of sound in seawater is 1.55 km/s, find the depth of the submarine.(b) Find its vertical velocity. (Take upward to be the positive direction.)

Well, for (a) I used the definition of velocity and multiplied 1,550 m/s by the time delay, .06s. My answer is 93m, which is wrong.

For (b), I utilized the equation v=lamba*f, where lambda is the wavelength and f is the frequency. Lambda is equivalent to (v+-u_s)/f_s, where u_s is the velocity of source relative to the medium, v is the velocity of waves in motion, and f_s is the frequency of the source. So v=((v+-u_s)/f_s)*f, where I assigned v=1550 m/s, u_s= 0 m/s, f_s = 29.958E6 Hz, and f=30E6 Hz. My answer is 1,552.17 m/s.

Please help!
 
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  • #2
krtica said:
A stationary destroyer is equipped with sonar that sends out pulses of sound at 30.000 MHz. Reflected pulses are received from a submarine directly below with a time delay of 60 ms at a frequency of 29.958 MHz.
(a) If the speed of sound in seawater is 1.55 km/s, find the depth of the submarine.

(b) Find its vertical velocity. (Take upward to be the positive direction.)

Well, for (a) I used the definition of velocity and multiplied 1,550 m/s by the time delay, .06s. My answer is 93m, which is wrong.
How is the distance traveled by the sound (down & back - hint, hint) related to the depth of the sub?
For (b), I utilized the equation v=lamba*f, where lambda is the wavelength and f is the frequency. Lambda is equivalent to (v+-u_s)/f_s, where u_s is the velocity of source relative to the medium, v is the velocity of waves in motion, and f_s is the frequency of the source. So v=((v+-u_s)/f_s)*f, where I assigned v=1550 m/s, u_s= 0 m/s, f_s = 29.958E6 Hz, and f=30E6 Hz. My answer is 1,552.17 m/s.

Please help!
For (b): The distance the sound waves travel changes at twice the rate at which the sub changes depth.
 
  • #3
Thank you, I found out what I was doing wrong.
 

Related to How Does the Doppler Effect Calculate Submarine Depth and Velocity?

1. What is the Doppler Effect and how does it relate to a destroyer?

The Doppler Effect is a phenomenon that occurs when there is a relative motion between a source of waves and an observer. In the case of a destroyer, the sound waves emitted by its engines are affected by the motion of the ship, resulting in a change in frequency or pitch of the sound heard by an observer.

2. How does the Doppler Effect affect sonar detection on a destroyer?

The Doppler Effect can impact sonar detection on a destroyer by altering the frequency of the sound waves emitted by the sonar equipment. This can make it more difficult to accurately detect and locate objects, as the reflected sound waves may have a different frequency than expected due to the motion of the destroyer.

3. Can the Doppler Effect be used as a defense mechanism on a destroyer?

Yes, the Doppler Effect can be utilized as a defense mechanism on a destroyer. By intentionally altering the frequency of the sound waves emitted by the ship's engines, the destroyer can create a false impression of its speed and direction to confuse potential enemies using sonar detection.

4. How is the Doppler Effect measured on a destroyer?

The Doppler Effect can be measured on a destroyer using specialized equipment such as Doppler radar or acoustic sensors. These devices can detect and measure the change in frequency of the sound waves emitted by the ship's engines, allowing for accurate calculations of the ship's speed and direction.

5. Can the Doppler Effect be used for navigation on a destroyer?

Yes, the Doppler Effect can be used for navigation on a destroyer. By measuring the change in frequency of the sound waves emitted by the ship's engines, the ship's crew can determine its speed and direction, which can be used for navigation purposes.

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