Wave Speed: Properties, Types, Formula and Examples

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Wave speed is defined as the distance travelled by a wave in a given unit of time. Alternatively, the number of meters travelled by a wave per second is the wave speed. Mostly the speed of the wave depends on the medium through which the wave is travelling. Generally, they travel faster in solids and slower in gases.

Wave speed is related to wavelength and wave frequency:

Wave Speed = Wavelength x Wave Frequency

Wavelength is the distance over which the wave shape repeats.
Whereas wave frequency is the number of waves that pass through a fixed point in a particular time frame.
Frequency is measured in Hertz and wavelength in meters.
Hence the unit of wave speed is meters per second.
It is also the SI unit of wave speed.

Table of Content

Definition of Wave
Types of Waves
Speed of Wave
Important Formulae
Things to Remember
Sample Questions

Key Terms: Wavelength, Frequency, Speed, Medium, Speed of light, Longitudinal wave, Transverse wave, Wavelength, SI units, Time period.

Definition of wave

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Disturbances that are caused from one point to another without any actual physical transfer or flow of matter is called a wave. A wave necessarily transfers energy between two points. For example:

The sound waves are produced in the air when we speak.
Water waves are produced when we throw pebbles into the water.
A medium is not necessarily needed for the waves to propagate.
Some waves can travel without a medium as well, e.g., electromagnetic waves.

Types of Waves

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Transverse and Longitudinal waves are the two different types of mechanical waves. All waves also have properties like period, frequency, amplitude, and so on. Discussed below are the types of waves and their properties.

Transverse and Longitudinal Waves

Mechanical waves require a medium to propagate. The oscillations produced in the medium are perpendicular to the direction of wave propagation; such a wave is called a transverse wave.

If the oscillations produced in the medium are in the direction of wave propagation such a wave is called a longitudinal wave.

Amplitude and phase of wave

Amplitude is the maximum displacement of the constituent of a medium from its equilibrium point or it can be said as the maximum positive or negative distance from the equilibrium point. Amplitude is by a or A. An example of amplitude is shown below:

Amplitude of Wave

Amplitude of Wave

Wavelength

Denoted by λ, the distance between two consecutive troughs or crests is the wavelength. The diagram representation is shown in the above figure.

Period, and wave frequency

The period of a wave is the time it takes for an element of a medium to complete one cycle, whereas the frequency of a wave is the number of oscillations in one second.

Wave period is measured in seconds (s) and frequency is measured in Hertz. (Hz)

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Speed of wave

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As mentioned above, the speed of the wave is the distance travelled by it in a particular time frame. To calculate the speed of the wave we wither directly use the formula

Speed of Wave = Distance/Time

The speed of the wave can also be calculated using the wavelength and the frequency.

Wave Speed = Wavelength x wave frequency

Both the deductions listed above will provide the same result.

A wave may propagate through a medium or vacuum.
Either way, the speed of the wave is calculated using the above results.
Also, the speed of the wave is decided by the medium in which the wave propagates.
If we compare light and sound waves, sound waves travel the slowest in gases and the fastest in solids.
The speed of a light wave, as it travels through a vacuum or air, is much faster than a sound wave.
The speed of the sound wave is 343.2 meters/second
The speed of the light wave is 3 x 10⁸meters/second
Unless, and until the medium is specified, we consider the speed of light to be 3 x 10⁸ meters/second.

Important Formulae

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The Important formulae used for the calculations of wave speed are given below

Speed of Wave = Distance/Time
Wave Speed = Wavelength x wave frequency
Frequency (f) = Speed of Wave (v) / wavelength (λ)
Period = 1 / frequency (f)
Speed of light = 3 x 10⁸ metres/second
Speed of sound wave = 343 metres/second

Things to Remember

The propagation of waves is basically energy transfer from one point to another. It must not be confused with the movement of matter. For example, in a sound wave and wind in air, sound wave energy is being transferred whereas in the case of a wind air traverses from one point to another.
Mechanical Waves require a medium to propagate.
Waves that do not require a medium to traverse are called electromagnetic waves. Examples of such waves are x-rays or light waves.
Mechanical waves can be classified into transverse waves and longitudinal waves.
In Transverse waves, constituents of the medium are perpendicular to the propagation of the wave.
In Longitudinal waves, constituents of the medium move along the direction of wave propagation.

Sample Questions

Ques. Sam stands 100 meters away from Echo Mountain. He shouts and a second later hears his echo. What will be the speed of the wave? (3 Marks)

Ans. The speed of the wave should be the sum of 200 m/s because the distance traveled by the sound wave in 1 second is equivalent to 100 meters to the echo mountain plus the 100 meters back from the mountain.

And, we know that,

Speed=Distance/Time

Putting the values above we get:

Speed =100 + 1001 second

=200 meters/second

Ques. A Light Wave Travels with a Wavelength of 200 nm. Calculate its wave Frequency. (3 Marks)

Ans. Wavelength λ given is = 200 nm

Now, we know the velocity of light (v) = 3 x 10⁸ m/s²

The frequency is calculated by the formula,

f = v/λ

Substituting the value of v and λ in the above formula, we get

f = 3×10⁸/200×10⁻⁹

f = 3×10⁸/2×10⁻⁷

f = 1.5 x 10¹⁵ Hz

Hence the frequency of the light wave is 1.5 x 10¹⁵ Hz

Ques. A light wave travels with the wavelength 300 nm, then finds out its frequency. (2 Marks)

Ans. The speed of light in Vacuum (v) is 3 x 10⁸ meters/second

Wavelength (λ) = 300 nm = 300 x 10⁹ metres

Frequency (f) = speed (v)/wavelength (λ)

=3 x 10⁸ / 300 x 10⁹

= 0.001 hertz (Hz)

Ques. A sound wave has a wavelength of 2.5 mm, then find out its frequency. (2 Marks)

Ans. Given wavelength λ = 2.5 mm

Now, we know the velocity of sound wave (v) = 343.2 m/s

Frequency is calculated using the formula

f = v/λ

Substituting the value of wavelength (λ) and velocity (v) in the above formula,

f = 343.2/2.5×10^-3

f = 137.28 KHz

Hence the frequency of the sound wave is 137.28 kHz

Ques. Listed below are different examples of wave motion. Select the one which is longitudinal, transverse, or both. (2 Marks)
(a) The liquid contained in a cylinder is moved back and through a piston
(b) A motor boat sailing in water

Ans.

Longitudinal
Both

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Maths MCQs	NCERT Class 11 Physics Book	Class 12 PCMB Notes
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