Wave Properties and Simple Harmonic Motion

Transverse vs. Longitudinal Waves

• Transverse waves: Oscillation perpendicular to propagation direction (e.g., light waves).
• Longitudinal waves: Oscillation parallel to propagation direction (e.g., sound waves).

Properties of Sound Waves

• Characterized by frequency, wavelength, amplitude, and speed.
• Speed depends on the medium's properties (density, elasticity).
• Can be reflected, refracted, diffracted, and superimposed.

Simple Harmonic Motion (SHM)

• Displacement: x = A sin(ωt + φ), where A is amplitude, ω is angular frequency, t is time, and φ is phase constant.
• Velocity: v = ωA cos(ωt + φ)
• Acceleration: a = -ω²A sin(ωt + φ) = -ω²x

Types of Vibrations

• Free vibrations: Oscillations without external force, determined by system's natural frequency.
• Forced vibrations: Oscillations driven by an external periodic force.
• Damped vibrations: Oscillations with energy loss, amplitude decreases over time.

Echo and Reverberation

• Echo: Reflection of sound wave creating a distinct, delayed repetition.
• Reverberation: Multiple reflections, creating a prolonged sound.

Optics Definitions

• Refractive index: Ratio of light's speed in vacuum to its speed in a medium.
• Total internal reflection (TIR): Complete reflection of light at a boundary when traveling from a denser to a less dense medium.
• Refraction: Bending of light as it passes from one medium to another due to change in speed.

Astronomical Telescope

• Construction: Uses objective lens (large focal length) and eyepiece lens (small focal length).
• Working: Objective lens forms a real, inverted image; eyepiece magnifies this image.
• Magnifying power: Ratio of the angle subtended by the image to the angle subtended by the object.

Optical Projection System

• Projects images onto a screen using lenses or mirrors.
• Components typically include light source, condenser, object, objective lens, and screen.
• Magnification adjustable depending on lens positions and properties.

Coulomb's Law

• Describes the force between two point charges: F = k|q1q2|/r², where k is Coulomb's constant, q1 and q2 are charges, and r is the distance between them.
• Force is attractive for opposite charges, repulsive for like charges.

Electric Concepts

• Electric field: Region around a charge where a force acts on another charge.
• Electric field lines: Visual representation of the electric field; direction indicates force on a positive charge.
• Electric potential: Potential energy per unit charge at a point in an electric field.
• Electric dipole: Two equal and opposite charges separated by a small distance.
• Electric flux: Measure of the electric field passing through a surface.

Electric Charge

• Fundamental property of matter; can be positive or negative.
• Quantized: exists in discrete units (multiples of electron charge).
• Conserved: total charge in an isolated system remains constant.

Gauss's Law

• Relates electric flux through a closed surface to the enclosed charge: Φ = Q/ε₀, where ε₀ is the permittivity of free space.
• Can be used to calculate electric fields for symmetrical charge distributions.
• Electric field due to an infinite line charge: E = λ/(2πε₀r), where λ is linear charge density and r is the distance from the wire.

Electrical Resistance

• Opposition to current flow in a conductor.
• Factors affecting resistance: material's resistivity, length, cross-sectional area, and temperature.

Resistor Color Coding

• System of colored bands on resistors to indicate resistance value and tolerance.
• Each band corresponds to a digit, multiplier, or tolerance.

Capacitance of Parallel Plate Capacitor

• C = ε₀A/d, where A is the area of plates, and d is the separation.

Equivalent Capacitance

• Series combination: 1/Ceq = 1/C1 + 1/C2 + ...
• Parallel combination: Ceq = C1 + C2 + ...

Faraday's Law of Electromagnetic Induction

• Induced electromotive force (EMF) is proportional to the rate of change of magnetic flux through a circuit.

Force on Moving Charge in Magnetic Field

• F = qvBsinθ, where q is charge, v is velocity, B is magnetic field strength, and θ is the angle between v and B.
• Force is perpendicular to both velocity and magnetic field.

p-n Junction Diode

• Formed by joining p-type and n-type semiconductors.
• Allows current flow in one direction (forward bias) and blocks it in the other (reverse bias).
• V-I characteristic shows a non-linear relationship.

p-type vs. n-type Semiconductors

• p-type: Majority carriers are holes (positive charge carriers).
• n-type: Majority carriers are electrons (negative charge carriers).

Laser

• Light Amplification by Stimulated Emission of Radiation.
• Properties: Monochromatic (single wavelength), coherent (waves in phase), and highly directional.

Ruby Laser

• Construction: Ruby crystal rod with mirrors at ends, flash lamp for excitation.
• Working: Pumping excites chromium ions; stimulated emission produces coherent light.

Numerical Aperture and Acceptance Angle

• Numerical aperture (NA): Measure of light-gathering ability of an optical fiber.
• Acceptance angle: Maximum angle at which light can enter the fiber and be guided. Related to NA.

This quiz covers the essential concepts of transverse and longitudinal waves, including properties of sound waves and simple harmonic motion. Additionally, it examines types of vibrations such as free, forced, and damped vibrations. Test your understanding of wave behaviors like echo and reverberation.