Calculating Wavelength and Expressions for Standing Waves | Homework Solution

[ee1215]

Homework Statement

A standing wave has been created on a string of length 1.5m. The frequency of the wave is 25Hz. The ends of the string are nodal points and there are 3 antinodes.
A)What is the wavelength of the standing wave?
B)If the maximum amplitude of the wave is 5cm, write complete expressions, including values for k and w, for the generated wave traveling to the right and the reflected wave traveling left. Take right as the +xˆ direction. (Hint: Remember the standing wave is the sum of two waves of equal amplitudes traveling in opposite directions.)

Homework Equations

omega=2pi*f
k=(2pi)/f

The Attempt at a Solution

A) L=(3*lambda)/2
so the wavelength = 1m

B) A=2.5cm = .025m
omega=2pi*f = 2pi(25) = 157 rad/s
k=(2pi)/h = 2pi/1 = 6.28m^-1

So in the right direction: y = 0.025cos(157t - 6.28x)
and the wave to the left is y = 0.025cos(157t + 6.28x)

Are these correct?

 

[ehild]

It looks all right, good job.

ehild