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Chapter 1: Sound
Introduction to Sound
Sound is a mechanical wave that requires a medium to travel. It is produced by vibrating objects and propagates through compressions and rarefactions in the medium.
Nature of Sound Waves
Sound waves are longitudinal waves where particles of the medium vibrate parallel to the direction of wave propagation.
Characteristics of Sound
- Pitch: Depends on frequency. Higher frequency = higher pitch.
- Loudness: Depends on amplitude. Greater amplitude = louder sound.
- Quality (Timbre): Distinguishes different sounds of same pitch.
Frequency (f) = 1 / Time Period (T)
Speed of Sound (v) = f × λ
Speed of Sound
v = √(E / ρ)
Where: E = modulus of elasticity, ρ = density
Speed of sound at 20°C in air: 343 m/s
Reflection of Sound
Sound reflects obeying the law of reflection: angle of incidence = angle of reflection.
- Echo: Reflected sound heard after 0.1s minimum
- Reverberation: Multiple reflections causing persistent sound
Ultrasound
Sound with frequency above 20,000 Hz (inaudible to humans).
Applications: Medical imaging, sonar, cleaning, welding
Chapter 2: Simple Harmonic Motion and Waves
Simple Harmonic Motion (SHM)
Motion where acceleration is directly proportional to displacement from mean position and always directed towards it.
F = -kx
Where: k = spring constant, x = displacement
Terms in SHM
- Amplitude (A): Maximum displacement from mean position
- Time Period (T): Time for one complete oscillation
- Frequency (f): Number of oscillations per second
- Phase: State of motion at any instant
f = 1/T
ω = 2πf = 2π/T
x = A sin(ωt + φ)
Simple Pendulum
T = 2π√(L/g)
Where: L = length of pendulum, g = gravitational acceleration
Wave Motion
- Transverse Wave: Particles vibrate perpendicular to wave direction (e.g., light, water waves)
- Longitudinal Wave: Particles vibrate parallel to wave direction (e.g., sound)
v = f × λ
Where: v = wave speed, f = frequency, λ = wavelength
Chapter 3: Geometrical Optics
Reflection of Light
When light strikes a surface and bounces back, it is called reflection.
Laws of Reflection
- Angle of incidence = Angle of reflection
- Incident ray, reflected ray, and normal all lie in the same plane
Types of Reflection
- Regular Reflection: From smooth surfaces (mirrors)
- Diffuse Reflection: From rough surfaces
Mirror Formula
1/f = 1/u + 1/v
Where: f = focal length, u = object distance, v = image distance
Magnification
m = -v/u = h'/h
Where: m = magnification, h' = image height, h = object height
Refraction of Light
Change in direction of light when passing from one medium to another.
Snell's Law: n₁ sinθ₁ = n₂ sinθ₂
n = c/v
Where: n = refractive index, c = speed in vacuum, v = speed in medium
Critical Angle
sin(C) = n₂/n₁
For total internal reflection when angle > critical angle
Lenses
1/f = 1/u + 1/v (Lens Formula)
P = 1/f (Power in diopters)
Convex vs Concave
- Convex (Converging): Thicker in middle, always forms real images (except when object is within focal length)
- Concave (Diverging): Thinner in middle, always forms virtual, upright, diminished images
Chapter 4: Electrostatics
Electric Charge
There are two types of electric charges:
- Positive Charge: Proton (lost electrons)
- Negative Charge: Electron (gained electrons)
Coulomb's Law
F = k(q₁q₂)/r²
Where: k = 9 × 10⁹ Nm²/C², q = charge, r = distance
Electric Field
E = F/q = kQ/r²
Direction: Away from positive, toward negative charge
Electric Potential
V = W/q = kQ/r
Unit: Volt (V) = Joule/Coulomb
Capacitor
Device that stores electric energy in an electric field.
C = Q/V
C = ε₀A/d (Parallel plate capacitor)
Energy Stored
U = ½CV² = ½QV² = Q²/2C
Chapter 5: Current Electricity
Electric Current
I = Q/t
Unit: Ampere (A)
Ohm's Law
V = IR
Where: V = voltage, I = current, R = resistance
Resistance
R = ρL/A
Where: ρ = resistivity, L = length, A = cross-sectional area
Resistivity
Resistance of a conductor of unit length and unit cross-section.
Series and Parallel Circuits
Series
R_total = R₁ + R₂ + R₃
I_same = I₁ = I₂ = I₃
Parallel
1/R_total = 1/R₁ + 1/R₂ + 1/R₃
V_same = V₁ = V₂ = V₃
Electric Power
P = VI = I²R = V²/R
Unit: Watt (W)
Joule's Law of Heating
H = I²Rt
Heat produced in a conductor
Chapter 6: Electromagnetism
Magnetic Field
Region around a magnet where magnetic force can be detected.
Biot-Savart Law
B = μ₀I/2πr
For straight conductor
Force on Current-Carrying Conductor
F = BIL sinθ
Where: B = magnetic field, I = current, L = length
Fleming's Left-Hand Rule
Thumb = Motion, First finger = Magnetic field, Middle finger = Current
Electromagnetic Induction
Production of EMF when magnetic flux changes through a coil.
ε = -dΦ/dt
Faraday's Law
Lenz's Law
Direction of induced EMF opposes the change causing it.
Transformers
V₁/V₂ = N₁/N₂ = I₂/I₁
Step-up: N₂ > N₁
Step-down: N₂ < N₁
AC Generator
ε = NBAω sin(ωt)
Converts mechanical energy to electrical energy
Chapter 7: Information and Communication Technology
Information and Communication Technology (ICT)
Use of technology for gathering, storing, retrieving, and communicating information.
Computer Fundamentals
- Hardware: Physical components (CPU, RAM, storage)
- Software: Programs and applications
- Data: Raw facts and figures
- Information: Processed data
Number Systems
- Binary: Base 2 (0, 1)
- Decimal: Base 10 (0-9)
- Hexadecimal: Base 16 (0-9, A-F)
Communication Technology
- Internet: Global network of computers
- Wi-Fi: Wireless local area network
- Bluetooth: Short-range wireless communication
- Mobile Networks: 4G, 5G cellular technology
Data Storage Units
1 Byte = 8 bits
1 KB = 1024 Bytes
1 MB = 1024 KB
1 GB = 1024 MB
1 TB = 1024 GB
Chapter 8: Atomic and Nuclear Physics
Structure of Atom
- Protons: Positively charged, in nucleus
- Neutrons: No charge, in nucleus
- Electrons: Negatively charged, orbit nucleus
Atomic Number and Mass Number
- Atomic Number (Z): Number of protons
- Mass Number (A): Protons + Neutrons
- Isotopes: Same Z, different A
Radioactivity
Spontaneous emission of particles or radiation from unstable nuclei.
Types of Radiation
- Alpha (α): Helium nucleus, +2 charge, least penetrating
- Beta (β): Electron, -1 charge, more penetrating
- Gamma (γ): High-energy photon, no charge, most penetrating
Half-Life
N = N₀(1/2)^(t/T)
Where: N = remaining nuclei, T = half-life
Nuclear Reactions
E = mc²
Einstein's mass-energy equivalence
Nuclear Fission
Splitting of heavy nucleus (e.g., Uranium-235) into lighter nuclei with release of energy.
Nuclear Fusion
Combining of light nuclei (e.g., Hydrogen) to form heavier nucleus with energy release. Powers the sun.
Key difference: Fusion releases MORE energy than fission but requires extremely high temperatures.
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