Speed of a Wave (Literal Wave)

Hypnos_16

1. The problem statement, all variables and given/known data

A jetskier is moving at 8.30 m/s in the direction in which the waves on a lake are moving. Each time he passes over a crest, he feels a bump. The bumping frequency is 1.17 Hz, and the crests are separated by 5.30 m. What is the wave speed?

Jetski's Speed = 8.30m/s with the waves
ƒ of waves= 1.17
wavelength = 5.30m

2. Relevant equations

v = (wavelength)ƒ

3. The attempt at a solution

when i tried the equation above i got an answer of 6.201m/s which turned out to now be right. What am i missing here?

v = ƒ(wavelength)
v = (1.17)(5.30)
v = (6.201m/s)

gneill

The waves are moving forward at the same time that the boat is, so the frequency of the bumps that the skier feels is not the frequency of the wave.

I suggest that you draw a diagram showing a wave at some starting time (zero is a good number), with the jetski at a wavecrest. The jetski will hit the following wavecrest at a time consistent with the given bump frequency. So, draw another wave below the first but shifted over to reflect that the wave has moved during that time interval. See if you can't work out the wave speed from there.

ehild

It is easy to solve this problem by using the relative velocity of the skier with respect to the waves. If the velocity of the waves is V, the relative velocity of the skier is 8.3-V (m/s), as they move in the same direction. You can imagine a standing wave pattern with crests 5.30 m apart. The skier travels this distance with its relative velocity in 1/f time (f is the frequency of the bumps). Just use the relation "distance = speed times time".

ehild

Hypnos_16

Why would it be 8.3 - V if they go in the same direction? wouldn't they add up? Also how does the skier have two relative velocities? (8.3 - v) and (1 / ƒ)
I'm still not getting it.

ehild

Imagine you sit on a train and another train travels beside you with the same velocity Does it seem moving at all?

The skier moves with velocity v(rel)=8.3-v during a time interval T=1/f. The distance travelled is 5.3 m.

ehild

Hypnos_16

Okay, yeah that makes sense now, i don't know how that didn't click before, thanks for your help man.