Home / Notes / Physics / Waves and Oscillations
Physics · Unit 6

Waves and Oscillations: MDCAT Notes and MCQs

Wave basics

  • A wave transfers energy (not matter) by a disturbance. Mechanical waves (sound, water, string) need a medium; electromagnetic waves travel through vacuum.
  • Terms: amplitude (max displacement), wavelength λ (crest to crest / compression to compression), period T, frequency f = 1/T. v = fλ.
  • Transverse: particles vibrate ⊥ to direction of travel — crests & troughs (string, light; can be polarized). Longitudinal: particles vibrate ∥ — compressions & rarefactions (sound, spring push-pull).

Speed of sound

  • Depends on elasticity and density of medium: v = √(E/ρ). Fastest in solids, then liquids, then gases (≈ 5000, 1500, 332 m/s).
  • Newton's formula (assumed isothermal): v = √(P/ρ) → ≈ 280 m/s in air at STP (≈ 16% too low).
  • Laplace correction (process is adiabatic): v = √(γP/ρ), γ = 1.4 for air → ≈ 332 m/s at 0 °C.
  • Factors: temperature (v ∝ √T; increases ≈ 0.61 m/s per °C rise), density (v ∝ 1/√ρ), humidity (moist air is less dense → faster). Pressure has no effect at constant temperature (P/ρ stays constant).

Superposition & interference

  • Principle of superposition: resultant displacement = vector sum of individual displacements.
  • Coherent sources: same frequency and constant phase difference. Constructive interference when path difference = nλ; destructive when path difference = (n + ½)λ.
  • Beats: two sounds of slightly different frequencies → periodic rise and fall of loudness; beat frequency = |f1 − f2|.

Stationary waves

  • Formed by superposition of two identical waves travelling in opposite directions. No energy transfer along the wave.
  • Nodes: zero displacement; antinodes: maximum displacement. Node-to-node = λ/2; node-to-antinode = λ/4.
  • Stretched string (fixed both ends): λn = 2L/n, fn = nv/2L, v = √(T/μ). All harmonics present; fundamental f1 = (1/2L)√(T/μ).
  • Open pipe (antinodes at both ends): fn = nv/2L — all harmonics.
  • Closed pipe (node at closed end): fn = nv/4L, n = 1, 3, 5 … — only odd harmonics.

Simple harmonic motion

  • Acceleration ∝ displacement and directed towards mean position: a = −ω²x.
  • Mass–spring: T = 2π√(m/k). Simple pendulum: T = 2π√(l/g) (independent of mass and small amplitude).
  • At mean position: max speed (vmax = ωx0), zero acceleration, max KE. At extremes: zero speed, max acceleration (ω²x0), max PE. v = ω√(x0² − x²). Total energy = ½kx0² (constant).
  • Projection of a particle in uniform circular motion on a diameter executes SHM: x = x0 cos ωt.
PMDC learning outcomes for this unit
  • Waves, sound, stationary waves, SHM: 6.1 Describe wave motion as illustrated by vibrations in ropes and springs.
  • Waves, sound, stationary waves, SHM: 6.2 Demonstrate that mechanical waves require a medium while electromagnetic waves do not.
  • Waves, sound, stationary waves, SHM: 6.3 Define medium, displacement, amplitude, period, compression, rarefaction, crest, trough, wavelength, velocity.
  • Waves, sound, stationary waves, SHM: 6.4 Solve problems using v = fλ.
  • Waves, sound, stationary waves, SHM: 6.5 Describe that energy is transferred due to a progressive wave.
  • Waves, sound, stationary waves, SHM: 6.6 Compare transverse and longitudinal waves.
  • Waves, sound, stationary waves, SHM: 6.7 Explain that speed of sound depends on the medium; describe Newton's formula.
  • Waves, sound, stationary waves, SHM: 6.8 Describe the Laplace correction in Newton's formula for speed of sound in air.
  • Waves, sound, stationary waves, SHM: 6.9 Identify the factors on which speed of sound in air depends.
  • Waves, sound, stationary waves, SHM: 6.10 Describe the principle of superposition of two waves from coherent sources.
  • Waves, sound, stationary waves, SHM: 6.11 Describe interference of sound waves.
  • Waves, sound, stationary waves, SHM: 6.12 Explain the formation of stationary waves using graphical method
  • Waves, sound, stationary waves, SHM: 6.13 Define the terms node and antinode.
  • Waves, sound, stationary waves, SHM: 6.14 Describe modes of vibration of strings.
  • Waves, sound, stationary waves, SHM: 6.15 Describe formation of stationary waves in vibrating air columns.
  • Waves, sound, stationary waves, SHM: 6.16 Explain the principle of superposition
  • Waves, sound, stationary waves, SHM: 6.17 Explain simple harmonic motion (SHM) and its characteristics.
  • Waves, sound, stationary waves, SHM: 6.18 Describe that the projection of uniform circular motion on a diameter is SHM.

Waves and Oscillations MCQs with answers

Practise and track your score →
Q1
A wave has frequency 50 Hz and wavelength 4 m. Its speed is:
A12.5 m/s
B54 m/s
C46 m/s
D200 m/s
Show answer
Answer: D (200 m/s). v = fλ = 50 × 4 = 200 m/s.
Q2
Sound waves in air are:
AStationary only
BTransverse
CLongitudinal
DElectromagnetic
Show answer
Answer: C (Longitudinal). Air particles vibrate parallel to the direction of propagation.
Q3
Which waves can travel through vacuum?
AWater waves
BWaves on a string
CElectromagnetic waves
DSound waves
Show answer
Answer: C (Electromagnetic waves). EM waves do not need a medium.
Q4
Newton's formula for the speed of sound in air gives a value of about:
A300 m/s
B340 m/s
C332 m/s
D280 m/s
Show answer
Answer: D (280 m/s). Assuming isothermal changes, v = √(P/ρ) ≈ 280 m/s.
Q5
Laplace corrected Newton's formula by assuming the propagation of sound is:
AIsobaric
BIsothermal
CIsochoric
DAdiabatic
Show answer
Answer: D (Adiabatic). Compressions/rarefactions are too fast for heat exchange → v = √(γP/ρ).
Q6
The speed of sound in air does NOT depend on:
ADensity
BPressure (at constant temperature)
CHumidity
DTemperature
Show answer
Answer: B (Pressure (at constant temperature)). P/ρ stays constant at constant temperature, so pressure has no effect.
Q7
The distance between two consecutive nodes in a stationary wave is:
A2λ
Bλ
Cλ/4
Dλ/2
Show answer
Answer: D (λ/2). Node-to-node separation = λ/2.
Q8
A pipe closed at one end produces:
AOnly odd harmonics
BNo harmonics
CAll harmonics
DOnly even harmonics
Show answer
Answer: A (Only odd harmonics). Node at closed end, antinode at open end → fn = nv/4L with n odd.
Q9
Two tuning forks of 256 Hz and 260 Hz sounded together produce:
A2 beats/s
B258 beats/s
C4 beats/s
D516 beats/s
Show answer
Answer: C (4 beats/s). Beat frequency = 260 − 256 = 4 Hz.
Q10
In SHM, acceleration is maximum at:
AEverywhere equal
BMidway
CMean position
DExtreme position
Show answer
Answer: D (Extreme position). a = −ω²x is maximum when |x| is maximum.
Q11
The time period of a simple pendulum depends on:
AMass of bob
BMaterial of bob
CAmplitude (large)
DLength and g
Show answer
Answer: D (Length and g). T = 2π√(l/g).
Q12
The projection of uniform circular motion on a diameter is:
ASimple harmonic motion
BUniform motion
CRandom motion
DProjectile motion
Show answer
Answer: A (Simple harmonic motion). The foot of the perpendicular oscillates with SHM.
← Fluid DynamicsThermodynamics →