410 marks

Oscillations and waves

This chapter covers simple harmonic motion and wave motion, including their equations and characteristics.

18 Topics

40h prep

3.3% subject weight

18 Topics

Kinetic and potential energies

2m2/10

📌 Key FormulaIn SHM, KE and PE vary with time, total energy constant.

Periodic motion

2m1/10

📌 Key FormulaMotion that repeats after a fixed time interval.

Period, frequency, displacement as a function of time

2m2/10

📌 Key FormulaT = 1/f, y = A sin(ωt + φ)

Periodic functions

2m1/10

📌 Key FormulaFunctions satisfying f(t+T) = f(t)

Simple harmonic motion (S.H.M.) and its equation

2m3/10

📌 Key FormulaF = -kx, a = -ω²x, x = A sin(ωt + φ)

Oscillations of a spring -restoring force and force constant

2m2/10

📌 Key FormulaF = -kx, k is force constant, T = 2π√(m/k)

Energy in S.H.M.

2m3/10

📌 Key FormulaK = ½kA² cos²(ωt+φ), U = ½kA² sin²(ωt+φ), E_total = ½kA²

Longitudinal and transverse waves

2m1/10

📌 Key FormulaLongitudinal: particle displacement along wave direction. Transverse: perpendicular.

Speed of a wave

2m1/10

📌 Key Formulav = fλ

Displacement relation for a progressive wave

2m3/10

📌 Key Formulay = A sin(ωt - kx + φ)

Principle of superposition of waves

2m2/10

📌 Key Formulay_net = y₁ + y₂

A reflection of waves

2m2/10

📌 Key FormulaReflection from rigid boundary (phase change of π), from free boundary (no phase change).

Standing waves in strings and organ pipes

2m4/10

📌 Key FormulaNodes and antinodes, frequency f = nv/(2L) for string, f = nv/(4L) for closed pipe, etc.

Fundamental mode and harmonics

2m3/10

📌 Key FormulaFundamental frequency, overtones, harmonics.

Beats

2m2/10

📌 Key FormulaBeat frequency f_beat = |f₁ - f₂|

Doppler Effect in sound

2m4/10

📌 Key Formulaf' = f (v ± v₀)/(v ∓ v_s)

Simple pendulum derivation of expression for its time period - Free, forced and damped oscillations

2m3/10

📌 Key FormulaT = 2π√(L/g). Damped: amplitude decreases, Forced: external periodic force, resonance.

Wave motion

2m1/10

📌 Key FormulaDisturbance propagation.

410 marks

Oscillations and waves

This chapter covers simple harmonic motion and wave motion, including their equations and characteristics.

18 Topics

40h prep

3.3% subject weight

18 Topics

Kinetic and potential energies

2m2/10

📌 Key FormulaIn SHM, KE and PE vary with time, total energy constant.

Periodic motion

2m1/10

📌 Key FormulaMotion that repeats after a fixed time interval.

Period, frequency, displacement as a function of time

2m2/10

📌 Key FormulaT = 1/f, y = A sin(ωt + φ)

Periodic functions

2m1/10

📌 Key FormulaFunctions satisfying f(t+T) = f(t)

Simple harmonic motion (S.H.M.) and its equation

2m3/10

📌 Key FormulaF = -kx, a = -ω²x, x = A sin(ωt + φ)

Oscillations of a spring -restoring force and force constant

2m2/10

📌 Key FormulaF = -kx, k is force constant, T = 2π√(m/k)

Energy in S.H.M.

2m3/10

📌 Key FormulaK = ½kA² cos²(ωt+φ), U = ½kA² sin²(ωt+φ), E_total = ½kA²

Longitudinal and transverse waves

2m1/10

📌 Key FormulaLongitudinal: particle displacement along wave direction. Transverse: perpendicular.

Speed of a wave

2m1/10

📌 Key Formulav = fλ

Displacement relation for a progressive wave

2m3/10

📌 Key Formulay = A sin(ωt - kx + φ)

Principle of superposition of waves

2m2/10

📌 Key Formulay_net = y₁ + y₂

A reflection of waves

2m2/10

📌 Key FormulaReflection from rigid boundary (phase change of π), from free boundary (no phase change).

Standing waves in strings and organ pipes

2m4/10

📌 Key FormulaNodes and antinodes, frequency f = nv/(2L) for string, f = nv/(4L) for closed pipe, etc.

Fundamental mode and harmonics

2m3/10

📌 Key FormulaFundamental frequency, overtones, harmonics.

Beats

2m2/10

📌 Key FormulaBeat frequency f_beat = |f₁ - f₂|

Doppler Effect in sound

2m4/10

📌 Key Formulaf' = f (v ± v₀)/(v ∓ v_s)

Simple pendulum derivation of expression for its time period - Free, forced and damped oscillations

2m3/10

📌 Key FormulaT = 2π√(L/g). Damped: amplitude decreases, Forced: external periodic force, resonance.

Wave motion

2m1/10

📌 Key FormulaDisturbance propagation.