A wave is described by the equation
(a) Find the time period and the wavelength?
(b) Write the equation for the velocity of the particles. Find the speed of the particle at at time
(c) What are the speeds of the particles at , and at ?
Step 1.Given data
Equation of wave …………
Step 2. Comparing the given equation to the general equation of the wave
General equation of the wave
where is amplitude of the wave
is the wave vector
is the angular frequency
Now, comparing the given equation to the general equation of the wave ,we get
Step 3. Finding the time period of the wave
By using the formula of the time period
Step 4. Finding the wavelength of the wave
By using the formula of the wavelength
Hence , the time period of the wave is and wavelength of the wave is
Step 1. Given data
Step 2. Finding the velocity of wave
If we derivate equation with respect to time then, we get
velocity ,
………..
Step 3. Finding the velocity at and
Now putting the given values in , we get
Hence the velocity at is
Step 1. Given data
Step 2. Finding the velocity at
Now putting in ,we get
Step 3. Finding the velocity at
Putting in , we get
Step 4. Finding the velocity at
Putting in , we get
Hence , velocity at is .