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

fertilizeki

fertilizeki

Answered question

2022-01-12

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?

Answer & Explanation

Melissa Moore

Melissa Moore

Beginner2022-01-13Added 32 answers

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:
ff+=1vsv
vsv=1ffs
v=vs(11ffs)
v=vs(fsfsf)
v=(1.5ms)(0.30Hz0.30Hz0.20Hz)=4.5ms

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