In the given progressive wave y=5sin100πt-0.4πx where y and x are in metre, t is in seconds. What is:

1. amplitude?

2. wavelength?

3. frequency?

4. wave velocity?

5. particle velocity amplitude? 

Hint: Use the standard equation of the wave.
Step 1: Compare the given equation with the standard equation of the wave.
The standard equation of a progressive wave is given by:
This is travelling along positive x-direction.
Given equation is, y=5sin100πt-0.4πx
Comparing with the standard equation;
1. Amplitude = 5m
2. k=2πλ=0.4π
    Wavelength, λ=2πk=2π0.4π=204=5m
                 Frequency, ν=100π2π=50Hz
4. Wave velocity, ν=ωk,where k is wave number and k=2πλ.
=250 m/s
dydt=particle velocity
From Eq. (i):
For particle, velocity amplitude=dydtmax
which will be for cos100πt-0.4πxmax=1
Particle velocity amplitude=dydtmax=5100π×1
=500 π m/s