How Long Does It Take for a Wave Point to Move Between Two Set Displacements?

[Matt H]

Homework Statement

If y(x, t) = (6.7 mm) sin(kx + (705 rad/s)t + ϕ) describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = -2.0 mm and y = +2.0 mm?

Homework Equations

I'm not sure where to start.

The Attempt at a Solution

That's the problem.

 

[Pyroadept]

Fix the value of x. Easiest value - take x = 0.

Then: y(0,t) = (6.7 mm) sin((705 rad/s)t)

Let y = -2 mm
Thus: 6.7sin(705t) = -2
Now solve for t.

Do the same for y = 2 mm

Subtract the two values (smaller from the larger) to find the time taken to go from one to the other.

 

[nlightner]

As a scientist, it is important to have a clear understanding of the problem before attempting to solve it. In this case, the problem is asking for the amount of time it takes for a point on a string to move between two specific displacements. To solve this, we can use the equation provided: y(x,t) = (6.7 mm) sin(kx + (705 rad/s)t + ϕ). This equation describes a wave traveling along a string, where x is the position along the string, t is the time, k is the wave number, and ϕ is the phase angle. In order to find the time it takes for a point on the string to move between two specific displacements, we need to set up an equation with the given displacements and solve for t. This can be done by setting y = -2.0 mm and y = +2.0 mm and solving for t. Once we have the value for t, we can determine the amount of time it takes for the point to move between the two displacements. It is also important to note that the value of k and ϕ may affect the time it takes for the point to move between the two displacements, so they should also be taken into consideration when solving the problem.