Suppose 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 ship that is moving away from the stationary ship?
http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/dopp.html
remember both out path and in path
To determine the speed of the ship that is moving away from the stationary ship, we can use the Doppler Effect equation:
Δf/f = v/c
Where:
Δf is the change in frequency (difference between emitted frequency and received frequency)
f is the emitted frequency
v is the velocity of the source (ship)
c is the speed of sound in the medium (sea water)
In this case, the emitted frequency (f) is 1400Hz, and the received frequency is 1390Hz. The speed of sound in sea water (c) is 1500m/s.
First, let's find the change in frequency (Δf):
Δf = Received frequency - Emitted frequency
Δf = 1390Hz - 1400Hz
Δf = -10Hz
Now we can substitute the values into the Doppler Effect equation:
-10Hz / 1400Hz = v / 1500m/s
Next, let's solve for v (velocity of the ship):
-10 / 1400 = v / 1500
Cross-multiplying:
-10 * 1500 = v * 1400
-15000 = 1400v
v = -15000 / 1400
v ≈ -10.71 m/s
Note: The negative sign indicates that the ship is moving away.
Therefore, the speed of the ship that is moving away from the stationary ship is approximately 10.71 m/s.