# Tranverse velocity of a point on a string

## 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?

## The Attempt at a Solution

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

collinsmark
Homework Helper
Gold Member
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.)?

"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
Homework Helper
Gold Member
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.

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?

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

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

ehild

SammyS
Staff Emeritus