The Wave Equation – Learn


The wave equation relates the velocity, frequency and wavelength of a wave. It can also be useful to incorporate the relationship between the period of a wave and its frequency.

Period and frequency: The period of a wave is inversely proportional to its frequency.

T=\cfrac { 1 }{ f } and f=\cfrac { 1 }{ T }

Where:

T = period of the wave in s (seconds)

f = frequency of the wave in Hz (Hertz)


Velocity, frequency, period and wavelength: The relationship between velocity, frequency, period and wavelength is represented by the following:

v=f\lambda and v=\cfrac { \lambda }{ T }

Where:

v = velocity of the wave in { m }/{ s }

\lambda = wavelength in m (metres)

T = period of the wave in s (seconds)

f = frequency of the wave in Hz (Hertz)


Example 1:

What is the velocity of a wave with a wavelength of 2.0 m and a frequency of 10 Hz?

\lambda =2.0

f =10

v=f\lambda

v=10\times 2

v=20{ m }/{ s }


Some questions will require the wave equation to be rearranged:

Example 2:

What is the frequency of a wave with a wavelength of 0.05 m and a velocity of 25{ m }/{ s } ?

\lambda =0.005

v =25

v=f\lambda, rearranged to give: f=\cfrac { v }{ \lambda }

f=\cfrac { 25 }{ 0.05 }

f=500Hz


Some questions will require the units to be changed:

Example 3:

What is the velocity of a wave with a wavelength of 740 nm and a frequency of 400 kHz?

\lambda =740nm740\times { 10 }^{ -9 }

f =400kHz400\times { 10 }^{ 3 }

v=f\lambda

v=(740\times { 10 }^{ -9 })\times (400\times { 10 }^{ 3 })

v=0.296{ m }/{ s }


Example 4:

What is the period of a wave with a frequency of 2.5 kHz?

f =2.5kHz2.5\times { 10 }^{ 3 }

T=\cfrac { 1 }{ f }

T=\cfrac { 1 }{ 2500 }

T=0.0004s

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