(a) write an equation describing a sinusoidal transverse wave traveling on a cord in the positive of a y axis with an angular wave number of a period of 0.20 s, and an amplitude of 3.0 mm. take the transverse direction to be the z direction.
(b) what is the maximum transverse speed of a point on the cord?
(c) what is the wave speed?

Missing data: the wave number

(a)  

For a transverse wave travelling in the positive y-direction and with vibration along the z-direction, the equation of the wave is

where

A is the amplitude of the wave

k is the wave number

is the angular frequency

t is the time

In this situation:

A = 3.0 mm = 0.003 m is the amplitude

is the wave number

is the period, so the angular frequency is

So, the wave equation (in meters) is

(b) 0.094 m/s

For a transverse wave, the transverse speed is equal to the derivative of the displacement of the wave, so in this case:

So the maximum transverse wave occurs when the cosine term is equal to 1, therefore the maximum transverse speed must be

where

Substituting,

(c) 5.24 mm/s

The wave speed is given by

where

f is the frequency of the wave

is the wavelength

The frequency can be found from the angular frequency:

While the wavelength can be found from the wave number:

Therefore, the wave speed is