Transverse harmonic wave Equation

[ctwokay]

Homework Statement

A transverse harmonic wave travels on a rope according to the following expression:
y(x,t) = 0.18sin(2.2x + 17.1t)
The mass density of the rope is μ = 0.146 kg/m. x and y are measured in meters and t in seconds.

Homework Equations

I do not know what to use.

The Attempt at a Solution

I tried to use change in wavelength / time but could not get the answer.
Tried to use v=f*lamda, and use T=1/f but no avail.

 

[Simon Bridge]

You have not given us a problem in your problem statement - what is it you are supposed to do?
Guessing you are trying to find the wave-speed. In which case, $v=f\lambda$ is correct - show your working.

The equation for y(x,t) has three numbers in it - do you know what they mean?

hint: $y(x,t)=Asin(kx-\omega t)$

 

[Redbelly98]

The mass density of the rope is μ = 0.146 kg/m.

I know of one and only one formula that makes use of the mass density of a rope or string. If you can find that formula (in your textbook or class notes), I'll bet it will be useful for solving this problem.

 

[Simon Bridge]

@Redbelly98: That's what I was wondering - if the object is to find the speed of the waves then the wave equation contains all the information needed so why include the mass-density (except as a red-herring)? But if the object is, say, to find the tension in the string - that's a different story.

 

[Redbelly98]

Agreed. The OP will need to tell us what the actual question is.

Be that as it may, the textbook should have a discussion of an equation like:

y(x,t) = 0.18sin(2.2x + 17.1t)

and how the velocity is related to that.

 

[Simon Bridge]

Indeed it should!
Though some text-books make a hash of it.
I don't want to assume anything though ... that would just make an *** out of u and me.
[huh: joke censored!]

Since the question is unknown, perhaps the answer is 42?

 

[ctwokay]

You have not given us a problem in your problem statement - what is it you are supposed to do?
Guessing you are trying to find the wave-speed. In which case, $v=f\lambda$ is correct - show your working.

The equation for y(x,t) has three numbers in it - do you know what they mean?

hint: $y(x,t)=Asin(kx-\omega t)$

I am trying to find the average speed of the rope during one complete oscillation of the rope

 

[ctwokay]

the average speed is change of displacement / period is that right?

 

[Redbelly98]

the average speed is change of displacement / period is that right?

That's the average velocity. Do they ask for average speed or average velocity?

 

[ctwokay]

That's the average velocity. Do they ask for average speed or average velocity?

They are asking for average speed

 

[Simon Bridge]

Each part of the rope has a speed in the x direction and a speed in the y direction.

For the y direction, displacement over time will give you zero, since, at the end of one period, the displacement is zero and part of the velocity is negative.

There are several ways to do this - directly: you get v_y(t) by -

$$v_y(t)=\frac{dy(t)}{dt}$$

You are given y(t), you can do the differentiation, so how would you go from v_y(t) to speed to average speed? The problem is to ensure your understanding of this.