# Homework Help: Using The Wave Equation To Solve A Question

1. Sep 12, 2015

### Ben.P

Hi,

In class a few days ago, my teacher gave me a challenge question which they wanted me to answer. I have yet to succeed in finding the correct answer so I would be grateful for anybody who might be able to explain where I am going wrong with this problem!

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

Here is the question: If four waves pass a stationary fishing boat every 8 seconds and the wave crests are 5m apart, what is the speed of the wave?

2. Relevant equations

• V = F x λ
(Wavespeed = Frequency x Wavelength)

• Frequency = 1/Time Period

3. The attempt at a solution

At first glance this question seemed very straight forward so I simply plugged the numbers into the formula!

V = F x λ
V = 1/8 x 5
V = 0.625 m/s

I then showed this working to my teacher, who said I was incorrect.
I have since been trying to figure out how else I could solve this problem, but have yet to come up with an answer.

I would be interested to see how you might tackle this question!

Many Thanks,
Ben

2. Sep 12, 2015

### TSny

Note that it takes 8 seconds for 4 waves to pass. How much time does it take for 1 wave to pass?

3. Sep 12, 2015

### Ben.P

1 Wave would take 2 seconds to pass... So would that mean that the wave travels at 2 m/s?

4. Sep 12, 2015

### TSny

No. It might help to remember the fundamental meaning of velocity (or speed). If something travels a certain distance in a certain time, how would you calculate the speed from the distance and the time?

5. Sep 12, 2015

### Ben.P

Speed = Distance/Time

So Then...

Speed = 5/8
Speed = 0.625 m/s

I still come out with the same answer.

6. Sep 12, 2015

### TSny

Yes, indeed. Try to use this.

7. Sep 12, 2015

### Ben.P

Check the post just above, edited it.

8. Sep 12, 2015

### TSny

You used 8 seconds for the time. How far does the wave train travel during 8 seconds?

9. Sep 12, 2015

### Ben.P

So for time I guess I would use 2? Also how could I figure how far the wave train travels during the 8 seconds if I don't have the speed yet. (D = S x T)

Unless I would do 5 x 8 = 40.

10. Sep 12, 2015

### TSny

You can use either 8 seconds or 2 seconds. If you want to use 8 seconds, then you will need to think about how far the wave moves in 8 seconds. Likewise for 2 seconds.

The problem statement gives you important information about what goes on during 8 seconds that should help you get the distance traveled in 8 seconds.

11. Sep 12, 2015

### TSny

I just now see that you edited post #9 by adding "Unless I would do 5 x 8 = 40".

EDITED: Yes, 40 m is correct incorrect for the distance traveled in 8 seconds. Hopefully, you are confident in this. The distance is not 40 m.

The problem statement would have been clearer if it had said, "If four wave crests pass a stationary fishing boat every 8 seconds and the wave crests are 5m apart, ..."

Last edited: Sep 12, 2015
12. Sep 12, 2015

### Ben.P

Ok I now confident with this, when you rephrased the question it helped! So I think this should now be correct:

S = D/T
S = 40/8
Speed of the Wave = 5 m/s

Also: How come we would use this method of solving rather than using V = F x λ?

13. Sep 12, 2015

### TSny

Sorry, the 40 m is wrong. Try again for how far the wave travels in 8 seconds. How much distance is taken up by 4 "waves" (i.e., 4 wavelengths)?

14. Sep 12, 2015

### Ben.P

This is where I have no ideas... My thoughts currently are that I have to do something with the 4 crests every 8 seconds but some how also use the information given in the question that the distance between each crests is 5 m.

EDIT: Might, Speed = Wavelength/Period be helpful?

15. Sep 12, 2015

### TSny

Maybe a sketch would help. Draw a wave such that a crest is located at the boat. Label some of the crests in your sketch as follows. Label the crest at the boat "crest 0". Pick out the next crest in your sketch that will pass the boat and label it "crest 1". How far from the boat is crest 1 in your sketch? That is, how far is crest 1 from crest 0? Let "crest 2" label the next crest after crest 1 that will pass the boat. Keep labeling several more crests. Which crest will be at the boat 8 seconds after the start?

16. Sep 12, 2015

### Ben.P

Ok, so I have gotten this far... I drew this out as well on a piece of paper, but how can you know what the wave will be at 8 seconds if we cannot calculate at what speed the waves are traveling at?

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17. Sep 12, 2015

### TSny

You are given that four "waves" pass the boat in 8 seconds. That means that four wave crests will pass the boat in 8 seconds. The figure below shows the wave at the initial time with crest "0" beside the boat. Which wave crest will be beside the boat 8 seconds later?

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18. Sep 12, 2015

### Ben.P

Crest number four would be beside the boat 8 seconds later

19. Sep 12, 2015

### TSny

Yes. How far does the wave have to travel in order for crest 4 to get to the boat?

20. Sep 12, 2015

### Ben.P

20 m because if I now know that it will take 4 crests and the distance between them is 5 meters. 4 x 5 = 20.

21. Sep 12, 2015

### TSny

Good. So, what is the distance traveled by the wave during 8 seconds?

22. Sep 12, 2015

### Ben.P

Isn't it 20m? Because surely now it's just a case of:

S = D/T
S = 20/8
S = 2.5 m/s

23. Sep 12, 2015

### TSny

Yes. That is correct.

For practice, you can see if you get the same answer using v = f λ where f is the frequency.
In your original post you wrote the formula f = 1/ (time period). You can use this to get the frequency if you know what the phrase "time period" means here.

24. Sep 12, 2015

### Ben.P

Ok, im glad I finally understood this. If you were given this problem could you possibly show me how you might have worked it out, as currently the steps it took me to understand seem very lengthy due to a lack of knowledge.

For time period is that not 8 seconds?

25. Sep 12, 2015

### TSny

If you look back over your solution, you can now see it is not really very lengthy.
In 8 seconds the wave travels 4 wavelengths.
Since each wavelength is 5 m, the wave travels 4 x 5 = 20 m during 8 seconds.
So, v = distance/time = 20 m/ 8 s = 2.5 m/s.

When calculating the frequency from f = 1/(time period) the phrase "time period" has a very special meaning. It is the time it takes the wave to travel one wavelength. In your problem, the time of 8 seconds is the time to travel four wavelengths.