Question

While anchored in the middle of a lake, you count exactly five 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 three waves are hitting the boat from behind every 10 s. what is the speed of the waves on the lake?

Answer 1

Every 10s 5 waves; t1 = 2s for each wave
When v = 1.5m/s, 3 waves in 10s t2 = 10 / 3s
Calculating the frequency in first case f1 = 5 / 10 = 0.5
Calculating the frequency in second case f2 = 3 / 10 = 0.3
Using the Doppler formula f = (1-v/c) f0
For the formula f = f2, v = velocity of boat= 1.5 m/s, f0 = f1, c is velocity of wave 0.3 = 0.5 x (1 - 1.5/c) => 1.5/c = 1 - 0.6 => 1.5/c = 0.4 => c = 1.5/0.4 Velocity of the wave = 3.75 m/s