Waves: Comprehensive NEET Physics Notes

1. Introduction to Waves

Waves are disturbances that transfer energy from one point to another without the transfer of matter. Examples of waves include sound waves, water waves, and light waves. In this chapter, we will focus on mechanical waves, which require a medium for propagation, such as air, water, or solids.

When a stone is dropped in water, the disturbance spreads in the form of circular waves. While the wave propagates outward, water particles do not move outward with the wave; instead, they oscillate up and down. This indicates that waves transport energy but not matter.

Did You Know?

Sound waves can travel through solids, liquids, and gases, but light waves can even travel through a vacuum.

2. Types of Mechanical Waves

2.1 Transverse Waves

In transverse waves, the particles of the medium oscillate perpendicular to the direction of wave propagation. An example is waves on a string. If you move one end of a stretched string up and down, the disturbance travels along the string, while the string particles move up and down.

2.2 Longitudinal Waves

In longitudinal waves, the particles oscillate parallel to the direction of wave propagation. Sound waves are the most common example, where compressions and rarefactions travel through the air.

Common Misconception:

Students often confuse the direction of particle motion with the direction of wave propagation. Remember that in transverse waves, particle motion is perpendicular, while in longitudinal waves, it is parallel to wave propagation.

Visual Aid Recommendation:
Include diagrams showing the motion of particles in transverse and longitudinal waves, with labeled directions of particle movement and wave propagation.

Quick Recap:

• Transverse waves involve perpendicular particle motion.
• Longitudinal waves involve parallel particle motion.
• Both wave types transfer energy without transferring matter.

3. Displacement Relation in a Progressive Wave

3.1 Mathematical Description of a Wave

A progressive wave can be described using the equation:

$y(x,t)=a\sin (kx-\omega t+\varphi )$

Where:

• $y(x,t)$ is the displacement at position $x$ and time $t$,
• $a$ is the amplitude,
• $k$ is the wave number,
• $\omega$ is the angular frequency, and
• $\varphi$ is the phase constant.

This equation represents a sinusoidal wave traveling in the positive x-direction.

NEET Problem-Solving Strategy:

For questions involving wave functions, identify the wave number, frequency, and phase from the equation. Ensure that you correctly determine whether the wave is moving in the positive or negative direction.

Visual Aid Recommendation:
Illustrate the graphical representation of a sinusoidal wave and mark the crest, trough, wavelength, and amplitude.

Quick Recap:

• Progressive waves are described by sinusoidal equations.
• Key terms: amplitude, wavelength, frequency, and phase.

4. Speed of a Traveling Wave

4.1 Wave Speed in a Medium

The speed of a wave in a medium depends on the properties of the medium. For a string, the speed is given by:

$v=\sqrt{\frac{T}{\mu }}$

Where:

• $T$ is the tension in the string, and
• $\mu$ is the linear mass density of the string.

For sound waves in air, the speed is given by:

$v=\sqrt{\frac{B}{\rho }}$

Where:

• $B$ is the bulk modulus of the medium, and
• $\rho$ is the density of the medium.

Real-life Application:

Understanding wave speed is crucial in designing musical instruments, where tension and mass density are adjusted to produce desired sound frequencies.

Quick Recap:

• Wave speed in a string depends on tension and linear mass density.
• Wave speed in fluids depends on bulk modulus and density.

5. Reflection and Superposition of Waves

5.1 Reflection of Waves

When a wave encounters a boundary, it can be reflected. If the boundary is rigid, the reflected wave undergoes a phase change of $\pi$. If the boundary is open, there is no phase change.

5.2 Principle of Superposition

When two or more waves meet, their displacements add algebraically. The superposition of waves can lead to constructive interference (amplitudes add up) or destructive interference (amplitudes cancel out).

Common Misconception:

Students often confuse the behavior of waves at rigid and open boundaries. Remember that rigid boundaries cause a phase change of $\pi$, while open boundaries do not.

Visual Aid Recommendation:
Include diagrams showing wave reflection at rigid and open boundaries, highlighting the phase changes.

Quick Recap:

• Waves reflect with a phase change at rigid boundaries.
• Superposition can lead to constructive or destructive interference.

6. Standing Waves and Resonance

6.1 Formation of Standing Waves

When two waves of the same frequency and amplitude travel in opposite directions, they form standing waves. The points of no displacement are called nodes, and points of maximum displacement are antinodes.

6.2 Resonance and Harmonics

In systems like strings and air columns, only certain frequencies produce standing waves. These are called natural frequencies or harmonics.

Real-life Application:

Resonance is used in musical instruments to amplify specific frequencies, producing clear and rich sounds.

Quick Recap:

• Standing waves have nodes and antinodes.
• Resonance occurs when a system vibrates at its natural frequency.

7. Practice Questions

1. A string is 1 m long and under a tension of 100 N. If the linear mass density is 0.01 kg/m, calculate the speed of a wave on the string.
2. A sound wave has a frequency of 500 Hz and travels through air at 340 m/s. What is its wavelength?
3. Explain why the speed of sound is higher in solids than in gases.
4. Two waves with the same amplitude but different frequencies interfere. What type of interference pattern is formed?
5. Calculate the first three harmonics of a string fixed at both ends if its length is 0.5 m and wave speed is 200 m/s.