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