While anchored in the middle of a lake, you count exactly three waves hitting your boat every 10 s. You raise anchor and start motoring slowly in the same direction the waves are going. When traveling at 1.5 m/s, you notice that exactly two waves are hitting the boat from behind every 10 s. What is the speed of the waves on the lake?

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Melissa Moore · Accepted Answer

Step 1  Solve for fs:  fs=3.010s=0.30Hz  When you are moving, the measured frequency is expressed as:  f−=2.010s=0.20Hz  By application of the equation f−=(1vsv)fs, we have:  f−f+=1−vsv  vsv=1−f−fs  v=vs(11−f−fs)  v=vs(fsfs−f−)  v=(1.5ms)(0.30Hz0.30Hz−0.20Hz)=4.5ms

While anchored in the middle of a lake, you count exactly three waves hitting your...

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