Bihar Board - Class 11 physics - Chapter 15: Waves Handwritten Notes

The chapter "Waves" focuses on the study of oscillatory disturbances that transfer energy through a medium or space without any net motion of the particles of the medium. Waves are fundamental in understanding phenomena in acoustics, optics, and electromagnetic theory. This chapter explains the nature, types, properties, and mathematical representation of waves.

Key Points

1. Types of Waves

   • Mechanical Waves: Require a medium for propagation, e.g., sound waves, water waves.
     • Transverse Waves: Particles vibrate perpendicular to the direction of wave propagation (e.g., waves on a string).
     • Longitudinal Waves: Particles vibrate parallel to the direction of wave propagation (e.g., sound waves).
   • Electromagnetic Waves: Do not require a medium and can propagate through a vacuum (e.g., light, radio waves).
   • Matter Waves: Associated with particles, as described in quantum mechanics.

2. Characteristics of Waves

   • Wavelength ($\lambda$): The distance between two consecutive crests or troughs in a wave.
   • Frequency ($f$): The number of oscillations per second.
   • Amplitude ($A$): The maximum displacement of particles from their equilibrium position.
   • Wave Speed ($v$): The speed at which the wave propagates through the medium. $$v = f\lambda$$
     

3. Wave Equation

   • A wave traveling in one dimension can be expressed as: $$y(x, t) = A \sin(kx - \omega t + \phi)$$where $k$ is the wave number ($k = \frac{2\pi}{\lambda}$), $\omega$ is the angular frequency ($\omega = 2\pi f$, and $\phi$ is the phase constant.

4. Types of Mechanical Waves

   • Progressive Waves: Continuously transfer energy through the medium.
   • Stationary (Standing) Waves: Formed by the superposition of two waves traveling in opposite directions, resulting in nodes (no displacement) and antinodes (maximum displacement).

5. Sound Waves

   • Sound is a longitudinal mechanical wave that propagates through a medium. Its speed depends on the medium's properties: $$v = \sqrt{\frac{B}{\rho}}$$ where $B$ is the bulk modulus and $\rho$ is the density of the medium.
   • The speed of sound is highest in solids, lower in liquids, and lowest in gases.

6. Superposition Principle

   • When two or more waves meet, the resultant displacement is the algebraic sum of their individual displacements. $$y_{\text{resultant}} = y_1 + y_2$$

7. Interference and Beats

   • Interference: The overlapping of two waves, resulting in constructive or destructive patterns.
   • Beats: Occur when two waves of slightly different frequencies interfere, creating periodic variations in amplitude.

8. Doppler Effect

   • The apparent change in frequency (or wavelength) of a wave due to the relative motion between the source and the observer. $$f' = f \frac{v + v_o}{v + v_s}$$where $f'$ is the observed frequency, $f$ is the source frequency, $v$ is the speed of the wave, $v_o$ is the observer's velocity, and $v_s$ is the source's velocity.

9. Reflection, Refraction, and Diffraction

   • Reflection: The bouncing back of a wave when it hits a barrier.
   • Refraction: The bending of a wave as it passes from one medium to another.
   • Diffraction: The spreading of waves when they pass through small openings or around obstacles.

10. Energy in Waves

    • The energy of a wave is proportional to the square of its amplitude. For a wave, energy is carried forward in the direction of propagation.

Conclusion

The chapter "Waves" provides insights into various wave phenomena and their mathematical descriptions. It builds a foundation for understanding complex concepts like acoustics, optics, and wave mechanics in future studies.

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