Question

Pepe and alfredo are resting on an offshore raft after a swim. they estimate that 3.00 m separates a trough and an adjacent crest of surface waves on the lake. they decide to determine the frequency of the waves by counting the number of wave crests which pass the raft in a given amount of time. they start the timer as soon as a crest passes them. they count 13.0 crests that pass by the raft in the next 20.2 s. calculate how fast the waves are moving.

Answer 1

The velocity (V) of a wave is the frequency (F) times the wave length (lambda):

     V =  F * lamda

lambda is the distance from crest to crest which is twice the distance from crest to trough.

=> lamba = 2 * 3.00 m = 6.00 m

F = number of waves / time = 13.0 waves / 20.2 s

Now you can plug in the values in the formula of V:

V = 6.00 m/wave* 13.0 waves / 20.2 s = 3.86 m/s

Answer: 3.86 m/s