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Question1: What is meant by wave motion?Define the terms wavelength and frequency and derive the relationship between them.

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Definition of wave motion


Wave motion
is the mechanism by which a disturbance at one point of the medium is propagated to another point in the surrounding and as a result of which energy is transmitted. The second point in the surrounding is always more away from the source generating the disturbance.

It is important to say that the material of the medium is not transferred along the disturbance.

Generally, the propagation of the disturbance is well organized in terms of wavelength, frequency and speed.Hence, the disturbance produced by the sound in air is called to be a wave. However, if we consider the disturbance produced by wind in the air, then it is not a wave. In the case of wind, the air molecules are also transferred from one point to another along the air current.

Another important aspect of wave motion is that waves transfer energy. In a traveling wave, one point disturbs another close point, imparting energy to it. The second point then disturbs another point adjacent to it and the process goes on.

Wave motion takes place in gases, liquids and solids. The electromagnetic type of waves can travel through space as well.

Definitions of wave length and frequency

Wavelength

If we closely observe a wave, there would be points throughout the wave pattern that are exactly in the same state of vibration.

The distance between any two successive points which are in the same state of vibration is called wavelength. For the sake of convenience, we say “it is the distance between any of its crest (or trough) to the next crest (or trough)”.

Frequency

It is the number of wave-cycles completed in one second. It is represented by ‘f’.

Relation between ‘f’ and ‘T’

Let a transverse wave travels in a stretched string. Time period is defined as “the time a wave takes to complete one cycle. It is represented by ‘T’ and measured in seconds.”

Similarly, “frequency is the number of waves completed in one second”.

Suppose 2 waves are completed in 1second. This means frequency of the wave is 2 cycles/sec.  Obviously, 1 wave will be completed in half second. This means the time period of the wave is ½ seconds. This gives us a simple relation between time period and frequency,

Suppose the wave is traveling with avelocity ‘v’ and it covers a distance Δx in time Δt. Then by the equation ofmotion,

Now if Δx = λ (one wavelength), Δt will be equal to ‘T’ (time period). So substituting in equation (1),  

Since 1/T = f,  therefore,

The above equation gives the relation between wavelength, frequency and speed of a wave.

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