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?

Question

Physics

Kenyon Good

26 October, 20:21

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?

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Kaylen · 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