Wave Formula

A wave is sensed when a source vibrates and disturbs a particle on the way in the medium. This can be seen in ripples in water when its surface is touched, in tuning fork, etc. This generates a wave pattern that starts to move along the medium from particle to particle. The frequency at which each particle vibrates is equal to the frequency at which the source vibrates. In one period, the source is capable of displacing the first particle upward from the rest, back to rest, downward from rest and finally back to rest. This whole back and forth motion makes one complete wave cycle. Every wave has its own wavelength, frequency, speed and time period.

The wave formula for the velocity of sound is given by,

V = f λ

Where,

v = velocity of the wave,

f = frequency of the wave,

λ = wavelength.

Solved Examples

Example 1

A light wave travels with a wavelength of 700 nm. Determine its frequency.

Solution:

Given:

Wavelength λ = 700 nm,

Velocity of light v = 3 x 10⁸ m/s

The frequency is calculated by,

f = v / λ

  = 3×10⁸ / 700×10^-9

f = 4.2 ×10¹⁴  Hz.

Therefore, the frequency of the light wave is 4.2 ×10¹⁴  Hz

Example 2: A sound wave has a wavelength of 2.5 mm. Determine its frequency.

Solution:

Given:

Wavelength λ = 2.5 cm,

Velocity of sound v = 343.2 m/s.

The frequency is calculated by,

f = v / λ

f = 343.2 / 2.5×10^-2

f = 13.72 kHz.

Therefore, the frequency of the sound wave is 13.72 kHz.