Uncovering the Vertical Velocity of a Wave

[ThirdEyeBlind]

Homework Statement

http://img683.imageshack.us/i/wave2.jpg/

The above figure shows height vs. displacement plot for a string which has a wave traveling to in the positive x direction at time t=2.5 sec with a velocity of 38 m/sec. What is the vertical (y) velocity of a piece of string at the point labeled 1?
vy= _____ cm/sec

Homework Equations

The Attempt at a Solution

The horizontal velocity at point 1 is zero so I figured the given velocity is the vertical velocity.

38 (m/s) * (100 cm/ 1 m) = 3800 cm/s but this is incorrect and I am out of ideas.

 

[anathema]

Thank you for sharing your thoughts and attempting a solution to this problem. Your approach is on the right track, but there are a few key concepts that need to be taken into consideration when determining the vertical velocity at point 1.

Firstly, it is important to note that the given velocity of 38 m/s is the overall velocity of the wave, not just the vertical velocity. This wave is a transverse wave, meaning that the particles of the string are oscillating up and down as the wave travels along the string. Therefore, the 38 m/s represents the combination of both the horizontal and vertical velocities at any given point on the string.

Secondly, the vertical velocity at point 1 is not equivalent to the overall velocity of the wave. This is because the vertical velocity at any point on the string is determined by the slope of the height vs. displacement curve at that point. In other words, the steeper the slope, the greater the vertical velocity.

So, to determine the vertical velocity at point 1, we need to look at the slope of the curve at that point. This can be done by drawing a tangent line to the curve at point 1 and calculating its slope. Alternatively, we can use the equation for the slope of a curve, which is dy/dx, where dy represents the change in height and dx represents the change in displacement.

Using this equation, we can calculate the vertical velocity at point 1 as follows:

vy = (dy/dx) * (dx/dt)

Where:
dy/dx = change in height/change in displacement = 2 cm/4 cm = 0.5 cm/cm
dx/dt = overall velocity of the wave = 38 m/s

Therefore, vy = 0.5 cm/cm * 38 m/s = 19 cm/s

So, the vertical velocity at point 1 is 19 cm/s.

I hope this helps to clarify the concept and solve the problem. Keep up the good work in your scientific studies!