Waves Representation and Terms

Transverse waves can generally be represented as shown below. It consists of series of crest and troughs. The direction of movement or vibration of particles is represented by y while the direction of movement or propagation of the wave is represented by x .

Longitudinal wave is made up of compression and rarefactions. The graph of longitudinal waves is the same with the graph of transverse wave .

Amplitude, A, of a wave

The amplitude of a wave is defined as the maximum displacement from the mean or rest position of the wave. The unit of amplitude is metre.

Period, T, of a wave.

The time required by a particle of a wave to complete an oscillation or to move one complete cycle is called the period, T of the wave. The unit of Period T is seconds. Since one cycle is the distance between two successive crests or two successive troughs, then period T is the time to move between two successive crests or two successive troughs. This is the time to travel one wavelength.

Frequency, f, of a wave.

This is the number of cycles the wave completes in one second. The unit of frequency is hertz (Hz). Larger units are kilohertz(kHz)= Hz, megahertz (MHz)= Hz and Gigahertz (GHz)= Hz

Wavelength, λ , of a wave.

The distance between two successive crests or two successive troughs is the wavelength of the wave. It is also the distance between successive compression or rarefaction in longitudinal wave.

The unit is in metre.  It is the distance covered after one complete cycle.

Speed, v, of a wave.

Speed of a wave or the wave speed is the distance which the wave travels in one second. It is measured in metres per seconds . 

Speed v of a wave = in   .  Where d is the distance covered by the wave in time t.  The speed of a wave is dependent on the properties of the medium through which the waves travel especially during refraction .

Expression relating T,f,v and λ

Period T is the time taken by the wave to complete or travel one cycle.

Lets assume it takes 4 seconds to complete one cycle. Then it will take 2 seconds to complete ½ cycle for the same wave. Hence it will take 1 seconds to complete ¼ cycle for the same wave.

By definition, frequency f is the number of cycles completed in 1 second for any wave. Therefore, the frequency for this wave will be ¼ hertz because ¼ cycle is completed in 1 seconds

We can then generalise that if period is T seconds, frequency f will be inverse of period T.

Mathematically,

T =    and f = .

Also speed v of a wave = in   .  Where d is the distance covered by the wave in time t.

When the distance covered by the wave is one wavelength , the time to cover one wavelength is the period T. wavelength is the linear distance covered during one cycle.

Speed v     

But f =

Therefore ,   

Examples

The distance between successive crests of a wave is 50cm. if the wave travels 60m in 4s , what is the frequency of the wave ?

V=60/4 = 15

Wavelength λ  = 50cm  = 0.5m

General Equation of Travelling Wave

A travelling wave with amplitude A and angular velocity ω can be represented in the form

But =

Also  

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