I don't understand this problem. Any help would be appreciated.
A sinusoidal wave can be described by the following function:
y(x,t) = (15.0 cm) cos( (0.157 m^-1)x + (50.3 s^-1)t + π/4 )
a) What are the amplitude, wave number, wavelength, and period of this wave?
b) Which way is the wave moving and how fast is it moving in that direction?
c) Draw a snapshot graph of the wave at t=0 seconds.
The general equation for a traveling wave is given by:
The wave number k is equal to 2*pi divided by the wavelength lambda therefore:
k=2*pi/lambda therefore lambda=2*pi/k=2*pi/0.157=40m
The angular frequency w is equal to 2*pi/T where T is the period, therefore:
The wave is moving towards the left since w*t is positive.
The velocity of the wave is equal to the product of the frequency and the wavelength:
But since period and frequency are mathematical inverses:
The wave speed becomes:
s=lambda/T=40m/0.125s=320m/s moving left