• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Speed of a Wave (Literal Wave)

  • Thread starter Hypnos_16
  • Start date
153
1
1. Homework Statement

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. Homework 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

Mentor
20,489
2,615
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

Homework Helper
15,360
1,766
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
 
153
1
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
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

Homework Helper
15,360
1,766
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
 
153
1
Okay, yeah that makes sense now, i don't know how that didn't click before, thanks for your help man.
 

Related Threads for: Speed of a Wave (Literal Wave)

  • Posted
Replies
4
Views
1K
  • Posted
Replies
1
Views
2K
Replies
3
Views
9K
Replies
15
Views
2K
Replies
4
Views
2K
Replies
1
Views
2K
Replies
4
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top