Some Terms Related with Waves

Crest and trough

When the displacement of a particle is maximum above from its mean position, the particle is said to be at the crest of the wave and when the displacement of a particle is maximum below the mean position, the particle is said to be at the trough. The transverse wave travels in the form of trough and crest.

Compression and rarefaction

TheLongitudinal wave travels in the form of compression and rarefaction. In compression, particles of medium get compressed and in rarefaction density is less than normal density. In another way, the region where the medium is compressed is known as a compression and the region where the medium is spread out is known as a rarefaction.

A complete wave

One crest and one trough constitute one complete wave in a transverse wave. One compression and one rarefaction constitute one complete wave in a longitudinal wave.

Amplitude (a)

The maximum displacement of a particle from its mean position in a wave is called amplitude of that wave. Its SI unit is ‘m’.

Frequency (f)

The number of complete waves, set up in a medium in one second is called frequency of the wave. Its SI unit is hertz (Hz).

Time period (T)

The time taken by wave to complete one cycle or a complete wave is called time period. Its unit is second.

Wavelength (λ)

The distance between two consecutive troughs or crests in a transverse wave or the distance between two consecutive compressions or rarefactions in a longitudinal wave is called wavelength. Its SI unit is meter (m).

Wave velocity (v)

The velocity with which wave propagates in a medium is called wave velocity. Its SI unit is m/s.

Wave equation

The formula showing the relation between v, f and λ is called wave equation. The product of frequency and wavelength is equal to wave velocity.

Wave velocity (v) = frequency (f) × wavelength (λ)

Relation between frequency (f) and time period (T)

The number of complete waves, set up in a medium in one second is called frequency of the wave. Its SI unit is hertz (Hz). According to the definition of frequency,
f vibrations are completed in one second.
Or, 1 vibrations is completed in \(\frac{1}{f}\) second.
But, time to complete one vibrationis its time period (T)
\(\therefore\) T = \(\frac{1}{f}\)