Sapose active sonar on a stationary ship is used to determine the speed of a ship that is moving away from it. A sonar ping is emitted at a frequency of 1400Hz, and the echo returns with a frequency of 1390Hz.The speed of sound in sea water is approximately 1500m/s. What is the speed of a ship that is moving away from the stationary ship?
use the doppler formula in your text.
To find the speed of the ship moving away, we need to use the Doppler effect. The Doppler effect states that the observed frequency of a wave is affected by the relative motion between the source of the wave and the observer.
In this case, the stationary ship is the observer, and the moving ship is the source. The difference in frequency between the emitted ping and the received echo can be used to determine the speed of the moving ship.
The formula to calculate the Doppler effect is:
f' = (v + vo) / (v + vs) * f
Where:
- f' is the observed frequency (in this case, 1390Hz)
- v is the speed of sound in water (1500m/s)
- vo is the velocity of the observer (the stationary ship, which is zero in this case)
- vs is the velocity of the source (the moving ship)
- f is the emitted frequency (1400Hz)
We need to solve for vs, the velocity of the source (the moving ship).
Let's rearrange the formula to solve for vs:
vs = (f * v - f * vo) / (f - f')
Plugging in the given values:
vs = (1400Hz * 1500m/s - 1400Hz * 0) / (1400Hz - 1390Hz)
Simplifying:
vs = (2100000m/s) / (10Hz)
vs = 210000m/s
Therefore, the speed of the ship moving away from the stationary ship is 210000 m/s.