Waves: Types, Properties, and Equations

Waves are a form of disturbance that travels through a medium due to repeated periodic motion of the particles of the medium about their mean positions.

• The disturbance is handed over from one particle to another particle of the medium without the actual movement of the particles of the medium.
• In a wave motion, disturbance travels through the medium but the medium does not travel along with the disturbance.
• In a wave, the energy is transferred from one point to another point of the medium.

Key Terms: Wave, Energy, Surface waves, Wave formula, Sound, Subatomic particles, Frequency, Wavelength, Compression, Rarefaction, Types of waves, Speed of sound

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Types of Waves

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Waves are classified as

• Mechanical waves or Elastic waves
• Electromagnetic waves
• Matter waves

Mechanical Waves

Mechanical waves require a material medium for their propagation.

• They cannot travel through a vacuum.
• Examples of mechanical waves are sound waves, water waves, waves in solid and liquid, seismic waves, etc.

Mechanical Waves are classified as

Transverse waves

Transverse waves are the waves in which the constituents of the medium oscillate perpendicular to the direction of wave propagation.

• Transverse waves can only propagate in solids and the surface of liquid.
• They cannot travel through gases and in the interior of the liquid.

Examples of transverse waves are

• A wave in a stretched string
• Ripples on the surface of water

Longitudinal waves

Longitudinal waves are the waves in which the constituents of the medium oscillate along the direction of wave propagation.

They can travel in all types of media i.e. solid, liquid, and gases.

Examples of longitudinal waves are

• Wave is produced when a spring rigidly fixed at one end is pulled and then left.
• Sound waves

Electromagnetic Waves

Electromagnetic waves do not require a medium for their propagation.

• They can travel through a vacuum.
• Examples of electromagnetic waves are X-rays, Radio waves, Light waves, etc.

Matter Waves

When a material particle like an electron, proton, neutron, atom, molecule, etc. moves, a wave is associated with these moving particles. This wave is known as Matter waves

Classification of Waves

Read More: Types of Radiation

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Properties of Wave[Click Here for Previous Year Questions]

The following are the properties of wave

• Amplitude: The amplitude of a wave is the magnitude of maximum displacement of the particles from their equilibrium position, as the wave passes through them.
• Wavelength: The distance between the two nearest points in a wave that is in the same phase of vibration is called the wavelength.
• Time Period: The time taken to complete one vibration is called time period (T).
• Frequency: The number of vibrations completed in one second is called the frequency of the wave.
• Velocity of Wave or Wave Velocity: The distance traveled by a wave in one second is called the velocity of the wave.

Wave class 11 notes pdf:

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Wave Speed Formula

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The formula for the speed of a traveling wave is given by

\(v = \frac {\omega}{k}\)

Where

• v is the speed of the traveling wave
• ω is the angular frequency
• k is the angular wave number

The formula for the speed of the transverse wave on a stretched string is given by

\(v = \sqrt {\frac {T}{\mu}}\)

Where

• T is the tension on the string
• μ is the linear mass density of the string

The speed of the sound wave in a medium is given by

\(v = \sqrt {\frac {\gamma P}{\rho}}\)

Where

• ρ is the mass density of the medium
• P is the pressure of the wave

Read More: Difference Between Scalar and Vector Quantities

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Superposition of Waves

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Two or more progressive waves can travel simultaneously in the medium without affecting the motion of one another.

• Therefore, the resultant displacement of each particle of the medium at any instant is equal to the vector sum of the displacements produced by two waves separately.
• This principle is called the principle of superposition.

Let us consider two transverse waves y₁ and y₂ of the same wavelength and amplitude traveling in the same direction, having the same angular frequency (ω) and a constant phase difference (ϕ). The displacement equation of both waves is given by

y₁ = A sin (kx – ωt)

y₂ = A sin (kx – ωt + ϕ)

From the principle of superposition, the resultant displacement is given by

y = y₁ + y₂

⇒ y = 2A cos (ϕ/2) sin (kx – ωt + ϕ/2)

Let a = 2A cos (ϕ/2), then

y = a sin (kx – ωt + ϕ/2)

Read More: Derivation of Escape Velocity

Interference

When two waves of the same frequency travel in a medium simultaneously in the same direction, then due to their superposition, the resultant intensity at any point of the medium is different from the sum intensities of the two waves.

• At some points, the intensity of the resultant wave is very large while at some other points, it is very small or zero.
• This phenomenon is called interference of waves.

Read More: International Systems of Units

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Reflection of Waves

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The rebounding back of waves when they strike a hard surface is called the reflection of the wave.

If the equation of incident traveling wave is

y(x, t) = a sin (kx - wt)

Equation of reflected wave

y (x, t) = a sin (kx + wt)

Echo

The repetition of sound caused by the reflection of sound waves at a distant surface, e.g., a cliff, a row of buildings, etc is called an echo.

• Sound persists in the ear for 0.1 s.
• The minimum distance from a sound-reflecting surface to hear an echo is 16.5 m.

Read More: Conservation Laws

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Things to Remember

• Waves are a type of disturbance that flows across a medium as a result of the repetitive periodic motion of the medium's particles about their mean positions.
• Mechanical waves, electromagnetic waves, and matter waves are the different types of waves.
• Mechanical waves are classified as Transverse waves and Longitudinal waves.
• A traveling wave is also known as a progressive wave.
• In longitudinal waves, the constituents of the medium oscillate along the direction of the wave.
• The speed of the longitudinal wave depends on the inertial property as well as the elastic property of the medium.

Also Read:

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Previous Year Questions

1. If the frequency of A is 530Hz, the original frequency of B will be :...[NEET 2020]
2. For what value of λ, is the maximum particle velocity equal to two times the wave velocity?...[NEET 1998]
3. If the frequency of the tuning for is 320Hz, the velocity of sound in air at 27^oC...[NEET 2018]
4. Where x is in meter and t in sec. The phase difference between them is...[NEET 2011]
5. When both the strings vibrate simultaneously the number of beats is :….[NEET 2009]
6. The equation of a wae is represented by y=10−4sin(100t−x10)m, then the velocity of wave will be...[NEET 2001]
7. If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is...[NEET 2001]
8. A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has….[NEET 1991]
9. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?….[NEET 2008]
10. The sum of the maximum and minimum intensities is….​[NEET 2008]
11. The change in wavelength of the radiation as received on the earth is...[NEET 1995]
12. The frequency of the echo as detected by the driver of the train is (Speed of sound in air is 330ms−1)..[NEET 2012]
13. Pick out the correct statement in the following with reference to stationary wave pattern​
14. If velocity of sound in air is 330ms−1, then the total number of resonances that occur will be​
15. Then the fundamental frequency of the open pipe is​
16. The apparent wavelength of sound in front of and behind the locomotive are respectively​
17.  The maximum particle velocity is equal to four times the wave velocity, if​
18. The distance between two nearest points which are 60^∘ out of phase is​