The Wave Equation - Learn - ScienceFlip

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?

$\lambda =740nm$ = $740\times { 10 }^{ -9 }$

$f =400kHz$ = $400\times { 10 }^{ 3 }$

$v=f\lambda$

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

$v=0.296{ m }/{ s }$

Example 4:

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

$f =2.5kHz$ = $2.5\times { 10 }^{ 3 }$

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

$T=\cfrac { 1 }{ 2500 }$

$T=0.0004s$