Wave Graphs

Displacement versus time graphs and displacement versus distance graphs are both useful ways of representing waves and the motion of particles in the wave medium. Both graphs illustrate the amplitude of the wave as displacement on the vertical axis.

Terminology:

Displacement (x): the distance that a particle is away from its rest, or zero displacement position.

Amplitude (A): the largest distance that a particle can be away from its rest, or zero displacement position.

Frequency (f): number of wavelengths that can pass a point in 1 second.

Wavelength (\lambda ): distance between successive crests or troughs.

Period (T): the time it takes for one wavelength to pass a point.

Wavenumber (k): number of wavelengths of a wave per unit length.

Note: The frequency of a wave is given by: f=\cfrac { 1 }{ T }

A displacement versus time graph is useful for determining the period, T, of a wave:

A displacement versus distance graph is useful for visualising the wavelength of a wave:

Wavenumber: The wavenumber of a wave refers to the number of waves per metre.

By definition: wavenumber, k=\cfrac { 2\pi }{ \lambda }

Example 1:

Use the wave graph below to answer the following:

a) What is the displacement at t=1 sec?

b) What is the amplitude of this wave?

c) What is the period of this wave?

a) Reading from the graph, at t=1 sec, displacement = 0 cm

b) Reading from the graph, amplitude = 2 cm

c) Reading from the graph, period = 0.8 sec

Example 2:

Use the wave graph below to answer the following:

a) What is the amplitude of this wave?

b) What is the wavelength of this wave?

a) Reading from the graph, amplitude = 0.4 cm

b) Reading from the graph, wavelength = 2 m 

Example 3:

What is the wavenumber of a wave which has a wavelength of 5 cm:

\lambda =5cm=0.05m

k=\cfrac { 2\pi }{ \lambda }

k=\cfrac { 2\pi }{ 0.05 }

k=125.7{ m }^{ -1 }