Waves is an important topic from NEET ExamPoint of view. Every year there are 1-2 questions directly asked from this topic. Some questions can be asked directly. This topic relates to our daily life, hence it is very easy to understand. This short notes on Waves will help you in revising the topic before the NEET Exam.

Notes on Waves

Waves: Wave is defined as the travelling disturbance with a well-defined speed along the medium.

1. Longitudinal and Transverse Waves

Wave Motion: Due to the vibration of the particles at their own position caused externally or internally, the disturbance (Wave) is transferred from particle to particle.

The wave basically carries the energy being transferred from one particle to the neighbouring particle.

Types of wave motion-Wave motion is mainly two types.

Transverse wave: The waves having the property where all the individual particles experience displacement perpendicular to the direction of the propagation of the wave. Transverse wave is generally harmonic wave i.e. either the wave general has the sine or cosine shape.

E.g.: Wave in a string, AC current, etc.

In case of waves in a string, any point on the string vibrates up and down with no horizontal motion at all. An individual point on the string oscillates with some amplitude as a wave travels past.

Longitudinal waves: The wave in which the particle experiences displacement parallel to the direction of the propagation.

E.g.: Sound waves, spring motion.

In the case of sound waves, the vibrations create a series of compressions and expansions and the wave travels along the compression in the direction of the propagation.

Note: Along with the transverse and the longitudinal waves some waves in nature demonstrate the combination of both such as Water wave.

Some phenomena occurring in nature cannot be described by a single moving wave instead of a complex combination of many travelling waves.

2. Terms related to Wave Motion

Amplitude (A) - It is defined as the maximum displacement of an oscillating particle of the medium from the mean position.

Wavelength (λ) - It is defined as the distance travelled by the wave during the time, the particle of the medium completes one oscillation about its mean position. Or the distance between two consecutive points in the same phase of wave motion. 

Time period (T) - It is defined as the time taken by a particle to complete one oscillation about its mean position. 

Frequency (f) - It is defined as the number of oscillations made by the particle in one second. 

Wave speed (v) - It is defined as the distance travelled by the wave in one second. Wave speed is v = fT, where f is the frequency and T is time period.

Phase-  The phase of a wave can be defined as the state of it which defines its position and the direction of its motion. It tells about the initial state of the wave.

Two particles if found in the same position having same velocities at every time instants, then they are said to be in the same phase or in-phase and if the particles have their displacements from the mean position and even velocity magnitude equal but are opposite in direction, the particles are said to be out of phase.

The intensity of the wave (I)- It is defined as the amount of energy flow per unit are per time in a direction perpendicular to the propagation of the wave. 

I = 2π²f²A²ρv, where f is the frequency of the wave, A is the amplitude, v is the wave speed, and ρ is the density of the wave.

Energy density (u) - It is defined as the amount of energy flow per unit volume. 

u = 2π²A²v²ρ, where A is the amplitude of the wave, v is the wave speed, and ρ is the density of the wave.

3. Displacement relation in a progressive wave

Progressive Wave- A wave that travels from one point of the medium to another is called the progressive wave. A progressive wave may be transverse or longitudinal.

The equation of progressive wave travelling along the +ve direction of wave is given by

, where y is the displacement o the particle at (x, t), A is the amplitude of the wave, ω is the angular frequency, k is the propagation constant or angular wave number, φ is phase constant.

Wave speed- It depends only on the nature of the medium in which the wave propagates. Wave speed, 

Particle speed- The speed of the particle in wave motion is,

Particle acceleration- The acceleration of the particle in wave motion is

4. Superposition of waves

If two or more waves travelling through a medium the resultant wave function at any point is the algebraic sum of the amplitude of all the individual wave functions. In superposition two travelling waves can pass through each other without being altered or without experiencing any change in their natural behaviour.

Fig. Phenomena of the superposition principle in a thread or rope for two waves and.

Three important cases, based on the principle of superposition are:

(a) Interference- Two waves of same frequency and hence wavelength, superpose and lead the phenomenon of interference.

The phenomenon of overlapping of the waves to produce a resultant wave in a space or region is known as Interference. There are two types of Interference:

Constructive Interference: If the amplitude displacement of the resultant wave is greater than the either of the individual pulses travelling in the same direction then the superposition is referred to as constructive Interference.

Destructive Interference:If the displacement caused by the waves are in opposite direction to each other the superposition is referred to as destructive interference and the resultant amplitude is smaller as compared to either of the individual pulses.

(b) Beats- When two waves of nearly equal frequencies travelling with same and moving in the same direction, superpose to each other give the phenomenon of beats.

Beat frequency- It is defined as the number of beats heard per second.

Beat frequency = Number of beats/second = difference in frequencies = f₁ - f₂

4. Stationary Waves

When two waves of the same frequency, wavelength and amplitude travel in opposite directions at the same speed, their superposition gives the stationary wave. Stationary waves are two types

The equation for a stationary wave is 

Stationary waves are characterized by nodes and antinodes.

Nodes are the points for which the amplitude is minimum whereas antinodes are the points for which the amplitude is maximum. In stationary wave nodes and antinodes are formed alternately and the distance between them is λ/4.

At antinodes, displacement and velocity are maximum. At nodes, displacement and velocity is zero. The distance between two consecutive nodes and antinodes is λ/2.

Vibration in a Stretched string of Length L fixed at both ends- The speed of transverse waves in a stretched string is, 

Where T is the tension in the string, and μ is the mass per unit length of the string.

For the first mode,  λ₁ = 2L and the fundamental frequency is 

For nth mode, 

The frequency of the nth mode is,

Closed Organ Pipe- In a closed organ pipe, one end is closed and another end is open. In a closed organ pipe, the closed end is always a node while the open end is always an antinode.

For the first mode, λ₁ = 4L, where L is the length of the pipe. 

Only odd harmonics are present in the closed organ pipe

For nth mode, 

Frequency, 

Open Organ Pipe- In an open organ pipe, both ends are open. In an open organ pipe, at both ends, there will be antinodes.

For the first mode, λ₁ = 2L, where L is the length of the pipe. 

 In open organ pipe, all harmonics are present, whereas in a closed organ pipe only odd harmonics are present.

For nth mode, 

Frequency, 

The fundamental frequency of an open organ pipe is twice that of a closed organ pipe of the same length. If an open pipe of length L is half submerged in water, it will become a closed pipe of length half that of the open pipe. So its frequency will become 

End Correction (e) -The antinode at the open end of a pipe is not formed exactly at the open end but a little outside. This is called the end correction. 

Due to the end correction, the fundamental frequency of a closed organ pipe is, 

Due to the end correction, the fundamental frequency of an open organ pipe is,

The speed of sound in air by resonance tube-Speed of sound in air at room temperature by using resonance tube is given by 

where v is the frequency of tuning fork, L₁ is first resonance length, and L₂is second resonance length.

End correction is 

5. Doppler effect

Doppler effect is the change in the observed frequency of a wave when the source and the observer O moves relative to the medium.

Case I- Source in motion but observer and medium at rest

When the source is moving towards the stationary observer  

Thus the source of sound approaches the observer the apparent frequency f' becomes greater than the true frequency f.

When the source moves away from a stationary observer

Thus the source of sound moves away from the observer the apparent frequency f' becomes less than the true frequency f.

Case II- Observer in motion, the source at rest, medium at rest

When the observer moves towards the stationary source

Thus when the observer approach towards the stationary source the apparent frequency f' becomes greater than the true frequency f.

When the observer moves away from a stationary source

Thus when the observer moves away from the source of sound then apparent frequency becomes less than true frequency .

Heat and Thermodynamics is an important topic from NEET Exam Point of view. Every year there are 1-2 questions directly asked from this topic.Some questions can be asked directly. This topic relates to our daily life, hence it is very easy to understand. This short notes on Heat and Thermodynamics will help you in revising the topic before the NEET Exam.

Heat and Thermodynamics

Thermodynamics: Thermodynamics is a branch of physics which deals with the relations of Heat and other forms of energy. It deals with the macroscopic variables such as temperature, pressure, and Volume.

Heat: Heat can be described as the transfer of energy between the objects, not the energy contained within the objects. Its SI unit is Joule (J). If heat absorbed by a system, then it is positive. But if heat is given out by a system then it is negative.

Temperature: Temperature is the measure of the degree of hotness and coldness of an object. On the macroscopic arena, the temperature is a physical property that governs the direction of heat flow between two objects placed in thermal contact. Heat always flows from the hotter object to the colder object. If no heat flow occurs, the two objects must have the same temperature.

Thermal equilibrium, Zeroth Law of Thermodynamics, Concept of Temperature

Thermal Equilibrium:  Two bodies when contact in each other and there is no flow of heat takes place, the bodies are said to be in thermal equilibrium.

Thermodynamic Systems: There are three types of thermodynamic systems.

Open System: In open system exchange of both energy and matter is possible between the system and surroundings.

Closed System: In closed system only, exchange of energy is possible between the system and surroundings.

Isolated System: In the isolated system there is no exchange of energy nor mass between the system and surroundings.

Zeroth Law of Thermodynamics: If two systems A and B are individually in thermal equilibrium with a third system C, then A and B are also in thermal equilibrium with each other.

Concept of Temperature: Zeroth Law of thermodynamics states that the temperature is a physical quantity having the same value for all systems which are in thermal equilibrium with each other.

Heat, Work and Internal Energy

Heat and Work: When mechanical work is converted into heat, the ratio of work done (W) to heat produced (Q) always remains the same and constant.

Here J is the joule constant.

Internal Energy: Internal energy is the sum of the kinetic and the potential energies of the molecules in a system observed in a frame of reference in which the center of mass of the system is at rest. Kinetic energy is a state parameter and depends only on the state of the thermodynamic system at that instance.

Heat Capacity: Heat capacity is defined as the amount of heat required to raise the temperature of a substance tone degree.

Specific Heat capacity:Specific heat capacity is the amount of heat required to increase the temperature of unit mass of the substance through one degree Celsius.

Molar Specific Heat:Molar specific heat is the amount of heat required to increase the temperature of one mole of the substance through one degree Celsius.

, where n is the number of moles.

Latent Heat: Latent heat is the amount of heat required to change the state of unit mass of a substance at constant temperature and pressure.

Latent heat of fusion:Latent heat of fusion is the required heat to change the state from solid to liquid.

Latent heat of Vaporization: Latent heat of Vaporization is required heat to change the state from liquid to gas.

Heat and Work:  Consider a gas container fitted with a movable piston. At equilibrium, the volume of the gas is V and it exerts a uniform pressure P on walls and on the piston. The piston has a cross-sectional area A, the force exerted by the gas on the piston is:

 F = PA

If the gas expansion undergoes a Quasi-static process i.e. it is slow enough so that the system remains in the thermal equilibrium.

The Work done by the gas is:

Under expansion: dV = +ve thus work done by the gas dW = -ve, and in compression both are negative.

First Law of Thermodynamics

First Law of Thermodynamics:  The heat energy supplied to the system increase the internal energy of the gas and the rest of the heat energy is converted into the work done by the system on the surroundings.

dQ = dU + dW

where dQ is the given heat, dU is the change in internal energy, and dW is the work done by the system.

Thermodynamic State Variables and Equation of State

Thermodynamic state Variables: Thermodynamic state of system is defined as the condition of the system at a specific time that can be identified using the appropriate set of variables known as thermodynamic state variables. State variables are also known as the state function.

For Example: Temperature pressure and Volume.

Equation of state: The equation of state is the mathematical expression for thermodynamics state, Pressure, Volume, and Temperature of a gas.

PV = nRT, where P is the pressure of gas, T is the temperature of the gas, V is the volume of gas, n is the number of moles, and   is the universal gas constant.

Thermodynamic Processes

Thermodynamic Process: There are various thermodynamic processes such as:

1. Quasistatic process: A very slow process and the system is always maintained in the thermal equilibrium.

2. Reversible Process: A process that can be made to reverse its direction of flow by changing the physical conditions and it is considered that there is no dissipation if energy.

3. Cyclic process: Any process where a system returns to its initial state. The change in the internal energy of the system is dU = 0.

4. Isochoric Process: A process in which the Volume is constant throughout.

Equation of state becomes  and the work done in isochoric process is, W = PdV = P×0 = 0

5. Isobaric Process: A process in which the pressure is constant throughout.

Equation of state becomes  and the work done in isobaric process is,

6. Isothermal Process: A process in which the temperature is constant throughout.

Equation of state becomes  and the work done in isothermal process is,

7. Adiabatic Process: A process where there is no heat exchange takes place between the system and the surrounding.

Work done = where  is the ration of specific heat at constant pressure and specific heat at constant volume.

8. Specific heat at Constant pressure:Amount of heat required to raise the temperature of one mole of gas by one degree of Celsius at constant pressure.

9. Specific heat at Constant Volume:Amount of heat required to raise the temperature of one mole of gas by one degree of Celsius at constant Volume.

Note: According to Mayer's law the difference between the specific heat at Constant Pressure and specific heat at Constant Volume is universal gas constant. 

For an Ideal Gas in Adiabatic process:

P-V diagram of the thermodynamic process:

Heat Engines: A heat Engine is a device that converts heat energy into a mechanical energy through a cyclic process.

Source or Hot Reservoir: It is a heat reservoir at higher temperature T_H .Theoretically, it is supposed to have the infinite thermal capacity so that up to any amount of heat can be drawn from it without changing its temperature.

Sink or Cold Reservoir: It is a heat reservoir at a lower temperature T_L . It has also infinite thermal capacity so that any amount of heat can be added to it without changing its temperature.

Heat Pump: Working part which performs mechanical work when heat is supplied to it for any matter (solid, liquid and gas).

Working: In every cycle of operation, the Heat pump absorbs a certain amount of heat Q₁ from the source at higher temperature T_H, converts a part of this heat energy into mechanical work W and rejects the remaining heat Q₂ to the sink at lower temperature environment. As the pump returns to its initial state after completing one cycle, there is no change in its internal energy.

Hence by the first law of thermodynamics, net heat absorbed in a cycle = Work done,

W = Q₂ - Q₁

Efficiency of Heat Engine: The ratio of the net work done by the engine in one cycle to the amount of heat absorbed by the pump from the source.

NOTE: Efficiency of any heat engine is always less than unity.

Second Law of Thermodynamics

Second Law of Thermodynamics:

Kelvin Planck Statement: It is not possible to design a heat engine working in a cyclic process and whose result is to take heat from a body at a single temperature and completely convert it into mechanical work.

Clausius Statement: It is not possible to design a refrigerator which works in a cyclic process and heat is transferred from a body to a higher temperature body.

Reversible and Irreversible Process: In a reversible process, the system can return to its initial conditions along the same path and every point along this path will be an equilibrium state.

A process that does not satisfy these requirements is irreversible.

Step 1-2: Isothermal Expansion: From 

Work done by ideal gas in this step is given by:

Step2-3: Adiabatic Expansion: From .

Work Done: 

Step 3-4: Isothermal Expansion: From 

Work Done: 

Step 4-1 Adiabatic Expansion: From 

Work Done:

Total Work Done: 

Carnot Efficiency:   Efficiency of a Carnot engine is,

Carnot Theorem: According to the Carnot Theorem, All Reversible engines operating between the same two temperatures have equal efficiency.

Refrigerator: A refrigerator works on the reverse principle of the Carnot heat engine.

It absorbs heat from the sink, the compressor in the refrigerator does the work and rejects the heat back to the source.

The coefficient of Performance: The ratio amount of heat removed to the mechanical work done on it in a cycle.