Calculate Speed, Freq & Wavelength of Transverse Waves

[v0rtexza]

Homework Statement

The distance between 10 consecutive crests of transverse waves is 360mm. A crest covers a distance of 40 mm in 2,5 seconds. Calculate the speed, frequency and wavelength of the waves.

Homework Equations

Period: The time taken for one complete vibration
Frequency: The number of complete vibrations per second
S = Speed
D = Distance
T = time
Speed = (distance/time) = (wavelength/period)
V = fλ
λ = wavelength
V= velocity
F = frequency = 1/period
period = 1/frequency

The Attempt at a Solution

f = 40/2,5 = 16
λ = 40 mm = 0,04
v = f * λ
v = 16 * 0,04
= 0,64 m/s

I just want to know if my calculations are correct or I am interchanging the wrong values.
Any help is appreciated, thanks!

 

[v0rtexza]

I looked at the question again and I think I solved it, I was calculating frequency wrong. f = 1/period and period is the time taken for one wave to move exactly one wavelength which is 2.5 seconds.

So f = 1/2.5 = 0.04
Then wavelength is 0.04 m
And finally v = fλ
so v = 0.04 * 0.04 = 0.016 m/s

I am fairly sure that I am correct but if not, please point it out to me!
Thanks again!

 

[berkeman]

Homework Statement

The distance between 10 consecutive crests of transverse waves is 360mm. A crest covers a distance of 40 mm in 2,5 seconds. Calculate the speed, frequency and wavelength of the waves.

Homework Equations

Period: The time taken for one complete vibration
Frequency: The number of complete vibrations per second
S = Speed
D = Distance
T = time
Speed = (distance/time) = (wavelength/period)
V = fλ
λ = wavelength
V= velocity
F = frequency = 1/period
period = 1/frequency

The Attempt at a Solution

f = 40/2,5 = 16
λ = 40 mm = 0,04
v = f * λ
v = 16 * 0,04
= 0,64 m/s

I just want to know if my calculations are correct or I am interchanging the wrong values.
Any help is appreciated, thanks!

No, it does look like you are mixing some things up.

Start with the wavelength. You are given how long 10 wavelengths are, so how long is one wavelength?

 

[Simon Bridge]

You got all of them wrong.
You appear to have been trying to remember equations instead of physics: concentrate on what the different things mean. eg.

v is the distance the wave travels divided by the time to travel.

λ is the wavelength - the distance between equal phase parts of the wave: the distance from crest-to-crest for example.

f=v/λ you realize.

 

[v0rtexza]

I believe that I realized my mistakes, is the second solution I posted above still incorrect?

 

[Simon Bridge]

I looked at the question again and I think I solved it, I was calculating frequency wrong. f = 1/period and period is the time taken for one wave to move exactly one wavelength which is 2.5 seconds.

That is not what it says. How far does the wave move in 2.5 seconds?
either you are assuming too much or you've missed out a step, I cannot tell from what you wrote.
How did you determine the wavelength?

I am fairly sure that I am correct but if not, please point it out to me!
Thanks again!

It still looks like you are thinking in terms of equations and not physics.

The wavelength is the distance from one crest to the next.
What is that distance?

 

[Simon Bridge]

Start with the wavelength. You are given how long 10 wavelengths are, so how long is one wavelength?

Technically, that's not true ... he's told how long 10 crests are. That is not really the same as 10 wavelengths.

eg. If I put a post in the ground every 2m and I put in 10 posts, how long is the line of posts?

 

[v0rtexza]

Ok well in that case, there are 10 consecutive crests so there is 9 wavelengths so I am told that the distance between all 10 crests is 360 mm so then 360/9 = 40 mm so the wavelength is 0.04 m?

 

[Simon Bridge]

That's the bit of information you need to put at the start.
(And hope the person writing the question didn't make the fence-post error.)

In each case you looked like you were working out the wavelength after the speed or the frequency - which makes everything look odd.

You are also told that the wave moves 40mm in 2.5s giving you speed as well as frequency. You can use v=fλ to check your results.

Note:
1. unless you are told to put all answers in SI units, it is acceptable to leave the units.
2. always put your reasoning - especially when seeking help online ;)