Tranverse velocity of a point on a string

[jegues]

Homework Statement

A sinusoidal wave is moving along a string. The equation governing the displacement as a function of position and time is,

$$y(x,t) = 0.12sin[8 \pi(t-\frac{x}{50})],$$

where x and y are in meters, and t is in seconds. At t = 2.4s, what is the transverse velocity of a point on the string at x = 5.0m?

Homework Equations

The Attempt at a Solution

I don't know how to get started on this one.

 

[collinsmark]

I don't know how to get started on this one.

"Transverse" means perpendicular to the string. The "transverse velocity" is not the speed of the wave. Rather it is the velocity of a tiny point on the string itself (attached to the string).

You are given the displacement of that point on a string, using the given equation,

$$y(x,t) = 0.12sin[8 \pi(t-\frac{x}{50})],$$

What's the relationship between displacement and velocity (in terms of integrals, derivatives, etc.)?

 

[jegues]

"Transverse" means perpendicular to the string. The "transverse velocity" is not the speed of the wave. Rather it is the velocity of a tiny point on the string itself (attached to the string).

You are given the displacement of that point on a string, using the given equation,

$$y(x,t) = 0.12sin[8 \pi(t-\frac{x}{50})],$$

What's the relationship between displacement and velocity (in terms of integrals, derivatives, etc.)?

Velocity is just $$\frac{dx}{dt}$$ isn't it?

 

[collinsmark]

Velocity is just $$\frac{dx}{dt}$$ isn't it?

dx/dt is the change in position per unit time (i.e. velocity) of something along the length of the string, assuming the string lies along the x-axis.

But a point on the string itself does not move along length of the string. It moves in a perpendicular, transverse direction. Specifically, it moves in the y direction. You're looking for dy/dt.

 

[jegues]

dx/dt is the change in position per unit time (i.e. velocity) of something along the length of the string, assuming the string lies along the x-axis.

But a point on the string itself does not move along length of the string. It moves in a perpendicular, transverse direction. Specifically, it moves in the y direction. You're looking for dy/dt.

Okay so,

$$\frac{dy}{dt} = 0.12 \cdot 8\pi cos(8 \pi t - \frac{8 \pi x}{50})$$

When I plug the numbers in I get,

$$\frac{dy}{dt} = 1.6m/s$$

Which is still incorrect?

 

[jegues]

Bump, still looking for help on finishing this one off!

 

[ehild]

Check the evaluation, if you did not mix radians with degrees.

ehild

 

[SammyS]

Bump, still looking for help on finishing this one off!

I got 2.868 m/s.