NEET Study Notes for Oscillations and Waves: Oscillations are the periodic to and fro movement of a body around the same point. This point is called equilibrium or the mean position. Waves are the disturbance propagation across any medium due to the repeated vibrations around the mean position.

• Periodic Motion is the repeated motion of a body after regular intervals of time. Such motions can be rectilinear, open/closed curvilinear.
• Examples of periodic motion are the motion of the moon around the earth, the motion of a simple pendulum.
• In NEET Physics Syllabus, Oscillation and Waves is an essential topic with at least 1-2 questions expected in NEET 2022.

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NEET Study Notes for Oscillations and Waves: Important Topics

NEET Study Notes on Oscillatory Motion

• When a body moves to and fro at regular intervals of time, repeatedly, and on the same point. This motion is called Oscillatory or Vibratory Motion.
• On either side of the mean position, the body is restricted within well-defined limits that are called extreme positions. Examples of Oscillatory or Vibratory Motions are the Motion of a ball in a bowl, the Needle of the sewing machine, the Pendulum of the clock, Child on a swing.
• All oscillatory motions are periodic motions but all period motions are not oscillatory.

Period and Frequency

The smallest interval of time, after which the oscillatory motions are repeated is called Time Period or T.

T= 2(pie)/angular velocity

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Frequency

The number of oscillations completed per unit of time is called the frequency. It is represented by v. S.I. Unit of Frequency of Frequency is Hertz.

where T is the time period

Amplitude

In either side of the mean position of the oscillating particle, the maximum displacement is called amplitude. Amplitude is denoted by A.

Phase

The parameter that is used to determine the position of the particle from the mean position is called Phase. Phase helps in the determination of the state of position and direction of the motion at a specific instant. The initial Phase is at which time is zero.

Displacement as a Function of Time-

The changes in physical quantities like position, pressure, angle with time is called Displacement. The displacement variable can have positive as well as negative values It is measured as a function of time.

Also Read:

• NEET Study Notes for Kinematics

• NEET Study Notes for Thermodynamics

NEET Study Notes on Simple Harmonic Function

If a particle moves in periodic motion, in a way that restoring force acts on a particle that is proportional to the displacement from the mean position. But in the opposite direction of the displacement, then this movement is called simple harmonic motion. Examples of Simple Harmonic Motion are the Motion of the body suspended by spring, oscillations of a simple pendulum.

There are two types of Simple Harmonic Motion

Linear SHM

When a particle is in linear SHM, it oscillates in a straight line repeatedly so that acceleration is proportional to displacement that is fixed from a point and is always directed towards that point.

i.e., F ∝ – x

or, 

where k = force constant

Angular SHM

When a body is in Angular SHM direction of angular velocity periodically changes and the torque that acts on it is always opposite and directed to angular displacement whereas the magnitude of the torque is directly proportional to the angular displacement.

 where C is called torsional rigidity

or, 

Characteristics of SHM

• Displacement- Displacement of particle in SHM is represented by 

where A- amplitude

ω- angular frequency

(ωt + φ)- phase of a particle at a point of time t.

• Velocity- Velocity of particle that is in SHM is represented by

 or, 

• Acceleration- The acceleration of particle that is in SHM is formulated by

a = – ω²y

• Energy- When a particle is in SHM, kinetic and potential energy varies between zero to maximum.

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Kinetic Energy Motion-

Potential Energy-

Total Energy in SHM- E = K.E. + P.E.

Free, Damped, Forced SHM and Resononance

Free Oscillation- Free Oscillation is the movement when there is no external force. Free Oscillations are also called natural frequency. Free SHM oscillation is

= F_{restoring force} = –kx,

K is constant

Damped Oscillation- When there is damped oscillation, the amplitude of the oscillating body reduces and eventually comes to its mean position.

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Forced Oscillations and Resonance

Free Oscillation- When the system oscillates without any external force on its own, the oscillations are called free oscillations.

Forced Oscillations- When a system oscillates due to an external force such oscillations are forced oscillations or driven oscillations. Differential equation of forced harmonic oscillation is

Displacement of the forced harmonic oscillator at time t is

where 

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• NEET Study Notes on Laws of Motion
• NEET Study Notes on Planar Motion

NEET Study Notes on Waves

When disturbance travels from one point of medium to another, however, there is no movement of particles. These could be electric potential, temperature, magnetic intensity. The medium should have inertia and electricity in order to travel. These properties also decide the speed of the wave. There are two types of waves:

Mechanical Waves

• Waves that require a medium to propagate are called Mechanical Waves Example of Mechanical Waves is Sound Waves.
• Non- Mechanical Waves- Non-Mechanical Waves or Electromagnetic Waves do not require any medium for propagation Examples- Lightwaves, Radio signals, X Rays,
• Mechanical Wave scan be classified into: Transverse Waves and Longitudinal Waves.

Transverse Waves

• In a transverse wave, the points in the medium oscillate in the direction that is perpendicular to the wave propagation direction.
• Transverse Waves can travel in solids and the liquid surface.
• In the form of crests and troughs, transverse waves propagate. The highest point in the wave is crest and the low point is trough.All electromagnetic waves are transverse.
• Examples of Transverse Waves are Lightwaves, torsion waves, water waves.
• Speed of Transverse Wave in solids is determined by 

where η- modulus of rigidity of solid

p= density of material

• Speed of Transverse Wave in stretched string= 

where T- tension in string

μ- mass per unit length of string

Longitudinal Waves

• In longitudinal waves, particle move in the same direction as that of the wave. Longitudinal Waves can travel in solids, liquids, and gases.
• Longitudinal waves propagate through compressions and refractions. Where the particles are close, it is called compressions.When the particles sre spread, it is called refractions.
• Examples of Longitudinal Waves are Sound Waves, p-yype earthquake waves and compression waves.
• Speed of longitudinal waves in solids is 

• Speed of longitudinal waves in liquids and gases is 

Speed of Sound in Gas

• By Newton’s Formula- 

where P - atmospheric pressure

P- density of air

• By Laplace’s Correction

where γ- ratio of specific heat C_p and C_v

NEET Study Notes on Principle of Superposition of Waves

When two or more waves arrive at a point simultaneously then net displacement at the point is the algebraic sum of individual wave displacement

y = y₁ + y₂ + ............... + y_n.

Here y1 and y2 is displacement caused by individual waves and y is the sum total of such displacement

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Beats

When two waves that differ in their frequency travel along the same path of straight line and same direction then the amplitude that results due to this will be maximum and minimum at alternate points in the medium. This process of waxing and waning sounds is called beats.

• The number of beats per second is 

where beat frequency = frequency difference of two interfering wave

Doppler Effect

Doppler Effect is the effect arising out of a situation where source of sound and observer are in relative motion to each other, the observer hears a frequency of sound that is different.

• The source is in motion and the observer at rest

Source movement is towards the observer- 

Source movement is away from observer- 

where V- velocity of sound

Vs- velocity of source

V0- source frequency

• Source at rest and observer in motion

When observer movement towards source

When observer movement away from source

Source and observer are in motion and moving away from each other

Source and observer are in motion and movement is towards each other

Read:

• NEET Study Notes on Ray Optics

• NEET Study Notes on Wave Optics

Reflection of Waves

• When mechanical wave reflects and refracts at a boundary, it operates as per the laws os reflection and refraction.
• A sound wave, on the other hand, reflects from a denser medium, wave experience a reversal phase of π. However, nature remains the same.
• Sound Wave when reflected from a rarer medium, the nature of the wave changes. However, there is no reversal in phase.

NEET Sample MCQs on Oscillation and Waves

Question: Restoring Force is proportional to the displacement of the body. What kind of motion is this?

1. Elliptical motion
2. Simple Harmonic Motion
3. Periodic Motion
4. Uniform Circular motion

Answer: Simple Harmonic Motion

Question: What is the circular motion of a particle with constant speed/

1. Simple harmonic motion but not periodic
2. Periodic and simple harmonic
3. Periodic but not simple harmonic
4. Neither periodic nor simple harmonic

Answer: periodic but not simple harmonic

Question: What is the restoring force acting on an object in SHM?

1. Inversely proportional to its velocity
2. Directly proportional to velocity
3. Inversely proportional to the displacement from mean position
4. Directly proportional to the displacement from mean position

Answer: Directly proportional to the displacement from mean position

Question: Which of the following is true about Simple harmonic motion?

1. In SHM, restoring force is directly proportional to velocity
2. In Sh, restoring force is directly proportional to angular velocity
3. In SHM, restoring force is directly proportional to displacement
4. In SHM, restoring force is directly proportional to square of displacement

Answer: In SHM, restoring force is directly proportional to displacement

Question: What is the frequency of the sound, when the observer remains stationary but the source is moving away?

1. Remains the same
2. It is halved
3. Reaches infinity
4. It gets doubled

Answer: It is halved

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