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physics waves formulas

What is wave?

Waves transport energy without transporting matter. The energy transportation is carried by a disturbance,which spreads out from a source. We are well familiar with different types of waves such as water waves in the ocean, or gently formed ripples on a still pond due to rain drop. When a musician plucks a guitar-string, sound waves are generated which on reaching our ear, produce the sensation of music. Wave disturbances may also come in a concentrated bundle like the shock waves from an aeroplane flying at supersonic speed. What ever may be the nature of waves, the mechanism by which it transport energy is the same. A succession of oscillatory in the vibrating body and propagation of wave through space is by means of oscillations.

Following are three types of waves:

  • Mechanical waves
  • Electromagnetic waves
  • Matter waves

Mechanical waves:

The waves which require a material medium for their propagation are known as mechanical waves

Examples: Water waves, sound waves.

Electrical Waves:

The waves which require no material medium for their propagation are called electromagnetic waves. These waves propagate out in space due to oscillation of electric and magnetic fields.

Examples: Light waves,Heat waves,radio waves.

Matter Waves:

A moving particle carries energy from one place to another in the form of kinetic energy.Since energy is carried by waves, therefore the waves associated with such moving particles are known as matter waves.

Progressive waves:

Drop a particle in water.Ripples will be produced and spread out across the water.The ripples are the examples to progressive waves because they carry energy across the water structure. A wave which transfers energy by moving away from the source of disturbance, is called a progressive or travelling wave.There are two kinds of progressive waves – transverse waves and longitudinal waves

Types of Progressive Waves:

There are two types of waves,i.e., transverse waves and longitudinal waves.

Transverse Waves:

A wave in which particles of the medium move perpendicularly to the direction of the wave is called a transverse wave. Waves that are produced in water are transverse waves. Observes transverse waves produced by the up and down movement of a rope. The highest point of a transverse wave is called crest, and the lowest point between two crests is called Trough.transverse wave

Longitudinal waves:

A wave in which particles of a medium move back and forth, parallel to the direction of the wave is called a longitudinal wave.If we pull and push one end of the slinky spring continuously, we can produce a longitudinal wave.

longitudinal wave

The part of a longitudinal wave, where particles of the medium are compressed together, are called compressions. The part of a longitudinal wave, where particles of the medium are spread out, are called rarefactions. As the wave moves, compressions and rarefactions are produced due to the back and forth motion of particles of the medium. Sound from a vibrating body produces longitudinal waves in air. These waves reach our ear and effect the ear drum.

Sound Waves are Longitudinal Waves:

A sound wave travelling through air is a an example of a longitudinal wave. When a drummer beats a drum, the surface of the drum vibrates and creates a disturbance in the air beside it.

When the drumhead moves to the left, it compresses the particles of air and create a compression. When the drumhead moves to the right, the particles of the air on the right move farther apart, create a rarefaction. These compressions and rarefactions travel through the air as longitudinal waves. When the disturbance in the air reaches our ears, we hear the sound of the drum.

Wavelength, Speed,Amplitude,and Frequency:

The basics terms to understand waves are amplitude,wavelength,frequency and speed.


A wavelength is the shortest distance between two adjacent crests or troughs of a transverse wave. For longitudinal waves, it is the distances between two adjacent compressions or rarefactions. Wavelength is measured in meter (m).


Amplitude of a wave is the mixture distance of the particles of the medium from the rest position. We can also say that it is the height of the crest or depth of a trough (transverse wave) measured from the rest position. Amplitude is measured in meters (m).

amplitude of wave


The number of vibrations produced by a vibrating body in one second is called its frequency. Frequency is measured in units called hertz (Hz). When one wave passes in one second its frequency is 1 wave per second or 1 hertz.

frequency of wave


Imagine watching a flash or lightning and thundering of cloud. First we see the flash of lighting. A few seconds later we hear thunder. This happens because sound and light travel at different speeds. Light travels much faster than sound. Different waves travel at different speed. This distance a wave covers in units time is called its speed. Speed is measured in meter per second. Sound travels at different speed in different mediums.

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