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Wave motion and equation of waves.

A plane progressive harmonic wave is represented by the equation (see attached) where is the displacement in meters, t is the time in seconds and x is distance from a fixed origin in meters.

Determine the following wave properties, and where appropriate give units:

a) The amplitude
b) The direction of wave travel
c) The wavelength
d) The speed of the wave
e) The wave frequency
f) The maximum speed of wave oscillations at a particular point
g) The equation of a wave of twice the amplitude and twice the frequency traveling at the same speed but in the opposite direction

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A plane progressive harmonic wave is represented by the equation
where is the displacement in meters, t is the time in seconds and x is distance from a fixed origin in meters.

Equation of a wave:

A mechanical wave is generated by a source which oscillates simple harmonically.
As the source oscillates the nearby particles of the medium will also oscillate and one by one the particles will oscillate and the energy is carried out. The velocity with which the disturbance caused in the medium (simple harmonic) is transported is called wave velocity.

Let the particle of medium at origin oscillate such that its displacement is given by the equation

Where A is the amplitude and  ...

Solution Summary

The solution contains calculations for wave equations, amplitudes, frequency, wavelength, speed of wave etc.

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