# Chapter 13: Waves

Waves

All waves are caused by oscillations and all transfer energy without transferring matter. This means that a water wave can transfer energy to you sitting on the shore without the water particles far out to the sea moving to the beach.

Progressive Wave transfers energy form one position to another through a material or a vacuum. A wave can be described as progressive; this means it is moving outwards from the source.

Some of the characteristics of wave are:

1. Amplitude, A
The amplitude of a wave is the maximum displacement of the particles from the equilibrium position.
1. Wavelength, λ
The wavelength of a wave is the length of one whole cycle. It can be measured between two adjacent peaks through or any point on a wave and the same point one wave later.
1. Displacement
The distance of a point of the wave from its equilibrium position.
1. Time period
It is the time taken for one complete oscillation of a point.
1. Frequency
It is the number of oscillations per unit time of a point.

F=1/T

Types of wave

1. Longitudinal wave
The waves in which the particles of the medium vibrate parallel to the direction of the wave velocity. E.g. sound wave
2. Transverse wave
The waves in which the particles of the medium vibrate at right angles to the direction of the wave velocity. E.g. electromagnetic and light waves Phase difference
Phase difference is the amount by which one oscillation leads or lags behind another.

Intensity of Wave
The intensity of a wave is defined as the rate of energy transmitted per unit area at right angle to the wave velocity.

intensity=power/(cross sectional area)

Relationship between Intensity and amplitude
Intensity ∝amplitude^2 (I α A^2)
It can also be written as, for a particular wave:
intensity/(amplitude ⌃2) = Constant
So, if one wave has twice the amplitude of another, it has four times the intensity.

Wave Equation
It is important equation connecting speed v of a wave with frequency f and wavelength λ can be shown as follow:
speed=distance/time i.e. v= λ/T
Wave speed= wavelength/period

Doppler Effect
You may have noticed the change in pitch of note heard when emergency vehicle passes you while sounding its siren. The pitch is higher when it approaches you and lower when it gets far from you. It is an example of Doppler Effect.

There are two different speeds involved in this situation:

• Source is moving with speed vs
• Sound waves travel through the air with speed v.

The frequency and wavelength will change according to speed vs

Observed frequency fo =(fs ×v)/(v±vs)

Where the plus sign applies to a receding source and the minus sign to an approaching source.

Electromagnetic Wave

An electromagnetic wave is a disturbance in the electric and magnetic field in space.

All electromagnetic wave travel at same speed of 3.0 × 108 ms-1 in a vacuum, but have different wavelengths and frequencies.

The regions of electromagnetic spectrum in order of increasing wavelength are: y-rays, X-rays, ultraviolet rays, visible rays, infrared rays, micro waves, and radio waves.