A Short Note on Variables Affecting Wave Speed

A wave is a disturbance in motion from one part of the medium to another. Waves can also be seen when a source or object vibrates and disturbs a particle present in the medium. It has various characteristic properties, such as amplitude, frequency, time period, speed, and wavelength. The speed of a wave depends on medium density and elasticity, temperature, and wavelength. The following article discusses these factors in detail.

What is Wave Speed?

The speed at which a wave travels in a given time period is known as wave speed. It can be calculated by the distance (in metres) it travels per unit time (in seconds). Wave speed depends on factors such as temperature, wavelength, and medium. The formula for wave speed is – v = f (λ), where f denotes wave frequency, v denotes velocity, and lambda symbolises wavelength.

Wave frequency is the number of waves that pass through a definite point in a given time period. The total measured distance between two consecutive troughs or crests of a wave is the wavelength. 

Compression is a point with the maximum density in a medium through which a longitudinal wave travels. In contrast, a rarefaction is a point with minimum density in a medium through which a longitudinal wave travels.

The Formula for Wave Speed

The speed of an electromagnetic wave, i.e. light, is – (3×108 m/s) in air. The unit for the speed of a wave is metres per second or (ms-1).

The derived formula for the speed of a wave can be illustrated as:

Speed = Distance/Time or Speed = Wavelength×Frequency

Variables Affecting the Speed of a Wave

The speed of a wave majorly depends on three factors:

• Wavelength – The speed is directly proportional to the wavelength. So, as the wavelength increases, the speed of the wave also increases, which can also be seen by the given formula:

λ × f = v

• Medium – The speed of electromagnetic waves changes according to the medium’s density and elastic nature. If the medium is denser, like glass, the light will travel slowly compared to the less dense medium, air.
• Temperature – High temperature leads to a higher rate of vibrations of the molecules. Thus, they can travel faster, such as in sound waves. The higher the temperature, the faster the wave’s speed rate in a given time period.

Properties of a Wave

The following are the specific properties of waves:

1. Amplitude (A):

It is the distance taken from the centre of the imaginary line to the bottom of the trough or tip of the crust. It can also be defined as the maximum distance or displacement covered by a wave or a point of a vibrating source from its equilibrium position. The energy of the wave is directly proportional to its amplitude. It is measured in metres (m).

2. Frequency (for v):

In simple words, the frequency of a wave is described as the number of times vibration occurs in a medium when a wave passes through that medium in a given amount of time. The wave frequency can be determined by calculating the number of crests that pass through a fixed point in a given time period. The higher the energy rate, the higher the wave’s frequency. The S.I. unit of frequency is Hertz (Hz).

3. Wavelength (λ): 

The distance between two consecutive troughs and crests of a wave is known as its wavelength. It is determined by the direction in which the wave is travelling. The wave can be of any type, whether a sound wave, electromagnetic wave, etc. As the wavelength is measured in the distance, the units for measurements can be in nanometres (nm), millimetres (mm), metres (m), or centimetres (cm). The longest wavelength is red, while the shortest wavelength is violet.

4. Time Period (T): 

The time taken by a particle in a medium to complete one vibrational cycle is called the time period of the wave. A period is a quantity of time, unlike frequency which is a rate quantity (cycles per second). The S.I. unit of the time period is seconds (s).

The equation can represent a sine wave equation:

y (0, t) = -a sin(wt.)

5. Speed (v):

Wave speed is the total distance travelled by a wave in a given time period. 

Let us consider sound waves in a fluid medium, such as air or water. Here, the speed is calculated by the formula – v = (B/ρ)1/2, where B represents the bulk modulus, and ρ denotes the density in kilograms per metre cube.

Take the example of longitudinal waves, such as sound waves passing through a thin rod. Its speed is calculated by the formula – v = (Y/ρ)1/2, where Y represents Young’s modulus, and ρ symbolises the density in kilograms per metre cube.

For transverse waves in a solid medium, the speed is calculated through the formula = (G/ρ)1/2, where G stands for shear modulus, whereas ρ denotes density in kilogram per metre cube.

The speed of the waves carried out by a string is measured via the equation – v = (T/μ)1/2, where T denotes tension in the string (newtons) and μ stands for mass per length (kg perm).

It is believed that electromagnetic waves do not need any medium to travel, which means that they can travel through a vacuum. The formula can determine their speed in a vacuum, c = (1/μo εo) 1/2 = 3.0×108 m/s, where the permeability constant is (μo), and the constant of free space of permittivity is εo.

Conclusion

The above article describes the terms wave speed, wave speed unit, and the different variables affecting wave speed. It also discusses the numerous properties of waves and the formula for calculating the speed of a wave. This article benefits the students preparing for national entrances, such as NEET and JEE mains/advances.