Wave Motion and Superposition
Progressive waves, speed of sound, principle of superposition, beats and standing waves. (Physics › Oscillations and Waves, NEET UG syllabus.)
What is Wave Motion and Superposition?
A wave that travels through a medium, transferring energy without net displacement of matter.
Key formula / rule: General Wave Equation
Key points
- Define and differentiate between transverse and longitudinal waves.
- Describe the characteristics of a progressive wave and write its general equation.
- Explain the factors affecting the speed of sound in different media.
- State and apply the principle of superposition to wave phenomena.
Common exam trap
Confusing transverse and longitudinal waves.
Definitions
- Term
Progressive Wave
- Meaning
A wave that travels through a medium, transferring energy without net displacement of matter.
- Term
Transverse Wave
- Meaning
A wave in which the particles of the medium oscillate perpendicular to the direction of wave propagation.
- Term
Longitudinal Wave
- Meaning
A wave in which the particles of the medium oscillate parallel to the direction of wave propagation.
- Term
Wavelength (λ)
- Meaning
The spatial period of a wave, the distance over which the wave's shape repeats.
- Term
Frequency (f)
- Meaning
The number of complete oscillations or cycles per unit time, measured in Hertz (Hz).
- Term
Amplitude (A)
- Meaning
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
- Term
Principle of Superposition
- Meaning
When two or more waves overlap, the resultant displacement at any point and time is the vector sum of the displacements due to individual waves.
- Term
Interference
- Meaning
The phenomenon where two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude.
- Term
Beats
- Meaning
Periodic variations in the intensity of sound caused by the superposition of two sound waves of slightly different frequencies.
- Term
Standing Wave
- Meaning
A wave formed by the superposition of two identical progressive waves traveling in opposite directions, appearing stationary with fixed nodes and antinodes.
- Term
Node
- Meaning
A point in a standing wave where the displacement is always zero.
- Term
Antinode
- Meaning
A point in a standing wave where the displacement is maximum.
- Term
Harmonic
- Meaning
A component frequency of a complex wave that is an integer multiple of the fundamental frequency.
Learning objectives
Define and differentiate between transverse and longitudinal waves.
Describe the characteristics of a progressive wave and write its general equation.
Explain the factors affecting the speed of sound in different media.
State and apply the principle of superposition to wave phenomena.
Explain the formation of beats and calculate beat frequency.
Describe the formation of standing waves and identify nodes and antinodes.
Derive and apply formulae for resonant frequencies in strings and organ pipes (open and closed).
Formulae
- Name
General Wave Equation
- Note
A: amplitude, k: wave number (2π/λ), ω: angular frequency (2πf), φ: initial phase
- Expression
y(x,t) = A sin(kx - ωt + φ)
- Name
Wave Speed
- Note
f: frequency, λ: wavelength, ω: angular frequency, k: wave number
- Expression
v = fλ = ω/k
- Name
Speed of Transverse Wave on a String
- Note
T: tension in the string, μ: linear mass density (mass per unit length)
- Expression
v = √(T/μ)
- Name
Speed of Sound in a Fluid
- Note
B: bulk modulus of the fluid, ρ: density of the fluid
- Expression
v = √(B/ρ)
- Name
Speed of Sound in an Ideal Gas
- Note
γ: adiabatic index, R: universal gas constant, T: absolute temperature, M: molar mass of the gas
- Expression
v = √(γRT/M)
- Name
Beat Frequency
- Note
f1, f2: frequencies of the two superposing waves
- Expression
fbeat = |f1 - f2|
- Name
Resonant Frequencies for String Fixed at Both Ends / Open Organ Pipe
- Note
n = 1, 2, 3... (n-th harmonic), v: wave speed, L: length of string/pipe
- Expression
fn = n(v/2L)
- Name
Resonant Frequencies for Closed Organ Pipe
- Note
n = 1, 2, 3... (only odd harmonics), v: wave speed, L: length of pipe
- Expression
fn = (2n-1)(v/4L)
Prerequisites
Basic understanding of oscillations and Simple Harmonic Motion (SHM).
Concepts of amplitude, frequency, time period, and wavelength.
Knowledge of basic trigonometry and wave functions (sine/cosine).
Common mistakes
Confusing transverse and longitudinal waves.
Incorrectly applying the superposition principle, especially for phase differences.
Calculating beat frequency as f1 + f2 instead of |f1 - f2|.
Misidentifying nodes and antinodes in standing waves or their positions.
Using the wrong formula for harmonics in open vs. closed organ pipes.
Assuming wave speed changes with amplitude or frequency (it depends on the medium).
Keywords
Wave
Progressive Wave
Transverse Wave
Longitudinal Wave
Wavelength
Frequency
Amplitude
Wave Speed
Speed of Sound
Superposition
Interference
Constructive Interference
Destructive Interference
Beats
Beat Frequency
Standing Wave
Node
Antinode
Harmonic
Overtone
Organ Pipe
Practice preview
Which of the following statements is true for a progressive wave?…
easy
A string fixed at both ends vibrates in its third harmonic. How many nodes and antinodes are present in the standing wave pattern?…
medium
Two waves are represented by the equations y1 = 5 sin(100pi t - pi x) and y2 = 10 sin(100pi t - pi x + pi/3). What is the amplitude of the resultant wave formed by their superposition?…
hard