Class 11 Physics: Waves Notes

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1. Introduction

• Wave: A disturbance that travels through a medium, transferring energy without transferring matter.
• Examples: Sound waves, water waves, waves on a string.

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2. Types of Waves

1. Mechanical Waves: Require a medium to propagate (sound, water waves, string waves).
2. Electromagnetic Waves: Do not require a medium (light, radio waves).
3. Matter Waves: Associated with particles (de Broglie waves).

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3. Classification of Mechanical Waves

1. Based on Direction of Oscillation:
   • Transverse Waves: Oscillation perpendicular to propagation (string wave, water surface).
   • Longitudinal Waves: Oscillation along propagation (sound waves in air).
2. Based on Dimensionality:
   • 1D, 2D, 3D waves (string, water, sound in air).

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4. Characteristics of Waves

• Wavelength (λ): Distance between two consecutive similar points (crests or troughs).
• Frequency (f): Number of oscillations per second.
• Time Period (T): Time for one complete oscillation, $T = \frac{1}{f}$T=f1​.
• Wave Velocity (v): Speed of wave propagation, $v = f \lambda$v=fλ.
• Amplitude (A): Maximum displacement from equilibrium.

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5. Wave Equation

• One-dimensional wave:

$$y(x,t) = A \sin(kx – \omega t) \quad \text{(travelling wave along +x)}$$y(x,t)=Asin(kx−ωt)(travelling wave along +x)

Where:

• $k = \frac{2\pi}{\lambda}$k=λ2π​ → wave number
• $\omega = 2\pi f$ω=2πf → angular frequency
• Wave speed:

$$v = \frac{\omega}{k} = f \lambda$$v=kω​=fλ

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6. Superposition of Waves

• Principle of Superposition: When two or more waves meet, their displacements add algebraically.
• Constructive Interference: Waves in phase → amplitude increases.
• Destructive Interference: Waves out of phase → amplitude decreases or cancels.

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7. Standing Waves

• Formed when two waves of same frequency and amplitude travel in opposite directions.
• Nodes: Points of zero displacement.
• Antinodes: Points of maximum displacement.
• Applications: Musical instruments, resonance in strings and air columns.

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8. Doppler Effect

• Definition: Change in frequency of a wave due to relative motion of source and observer.
• Formula (for sound):

$$f’ = f \frac{v \pm v_o}{v \mp v_s}$$f′=fv∓vs​v±vo​​

Where:

• $f$f = source frequency
• $f’$f′ = observed frequency
• $v$v = speed of sound
• $v_o$vo​ = speed of observer
• $v_s$vs​ = speed of source

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9. Key Points

• Waves transfer energy, not matter.
• Transverse vs Longitudinal: direction of oscillation differs.
• Standing waves: nodes and antinodes important in musical instruments.
• Wave speed depends on medium and wave type.