Using The Wave Equation To Solve A Question

[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!

Homework Statement

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?

Homework Equations

• V = F x λ

(Wavespeed = Frequency x Wavelength)

• Frequency = 1/Time Period

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

 

[TSny]

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

 

[Ben.P]

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

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

 

[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?

 

[Ben.P]

o. 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?

Speed = Distance/Time

So Then...

Speed = 5/8
Speed = 0.625 m/s

I still come out with the same answer.

 

[TSny]

Speed = Distance/Time

Yes, indeed. Try to use this.

 

[Ben.P]

Yes, indeed. Try to use this.

Check the post just above, edited it.

 

[TSny]

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

 

[Ben.P]

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

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.

 

[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.

 

[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, ..."

 

[Ben.P]

Yes, 40 m is correct for the distance traveled in 8 seconds. Hopefully, you are confident in this. 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, ..."

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?

 

[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)?

 

[Ben.P]

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)?

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?

 

[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?

 

[Ben.P]

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?

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?

 

[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?

 

[Ben.P]

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?

Crest number four would be beside the boat 8 seconds later

 

[TSny]

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

 

[Ben.P]

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

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.

 

[TSny]

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

 

[Ben.P]

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

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

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

 

[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.

 

[Ben.P]

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.

Ok, I am 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?

 

[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.

 

[Ben.P]

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.

Ok so if I understand correctly, I would need to use 2 seconds as my time period.

V = F x λ
V = 1/2 x 5
V = 2.5 m/s

 

[TSny]

Bingo!

 

[Ben.P]

Bingo!

Lovely! I must give you my sincere thanks for having helped me not only figure out the problem but assist me in understand why I need to do each step and how to do each step!

Once again, thank you so much for having helped me understand this.

Your Truly,
Ben

 

[TSny]

OK, Ben.

Welcome to PhysicsForums!

 

[Ben.P]

OK, Ben.

Welcome to PhysicsForums!

Thank you :)