JEE Main Physics Oscillations & Waves 2027: SHM, Standing Waves & Beats

A child on a swing, a guitar string, a tuning fork and an organ pipe all obey the same mathematics. Oscillations & Waves rewards students who spot that shared pattern: a restoring force proportional to displacement.

If the restoring force is proportional to displacement, it is simple harmonic motion.

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Chapter at a Glance

Priority reflects past-paper trends, not an official NTA weightage.

What the NTA Syllabus Covers

• Periodic motion, time period, frequency, displacement as a function of time
• Simple harmonic motion, phase, spring oscillations, energy in SHM, simple pendulum
• Wave motion, longitudinal and transverse waves, wave speed, progressive wave equation, superposition, reflection
• Standing waves in strings and organ pipes, fundamental mode and harmonics, beats

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Master These Topics

1. SHM Essentials

Displacement: x = A sin(ωt + φ). Velocity: v = ω√(A² − x²). Acceleration: a = −ω²x. The negative sign means acceleration always points towards the mean position.

• Spring-mass system: T = 2π√(m/k)
• Simple pendulum: T = 2π√(l/g)
• Springs in parallel: k = k₁ + k₂. In series: 1/k = 1/k₁ + 1/k₂.

Worked example: m = 0.5 kg, k = 200 N/m gives T = 2π√(0.0025) = 2π × 0.05 ≈ 0.314 s.

Total energy is E = ½kA², constant. Kinetic energy is ½k(A² − x²), and potential energy is ½kx². The two are equal at x = A/√2.

Trap: The period of a spring-mass system does not depend on g, so it stays the same on the Moon. A pendulum's period does depend on g.

2. Waves on a String and Standing Waves

Wave speed: v = fλ. On a stretched string, v = √(T/μ), where T is tension and μ is mass per unit length.

Worked example: Tension 100 N, μ = 0.01 kg/m gives v = √10⁴ = 100 m/s. For a string fixed at both ends with L = 1 m, the fundamental frequency is f₁ = v/2L = 50 Hz, and harmonics are f_n = n × 50 Hz.

3. Organ Pipes

• Open pipe: all harmonics, f_n = nv / 2L
• Closed pipe: only odd harmonics, f = (2n − 1)v / 4L

Worked example: A closed pipe of length 0.5 m with sound speed 340 m/s has fundamental 340 / (4 × 0.5) = 170 Hz. The next resonance is the third harmonic at 510 Hz.

4. Beats

Two nearby frequencies f₁ and f₂ superpose to give a beat frequency equal to their difference, f₁ − f₂. Tuning forks of 256 Hz and 260 Hz produce 4 beats per second.

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Common Traps to Avoid

• Using the wrong sign or phase when writing the SHM equation from initial conditions.
• Forgetting that closed pipes support only odd harmonics.
• Adding spring constants for springs in series. Series combines reciprocals.
• Mixing up amplitude, displacement and energy relations.

60-Second Revision Sheet

• ω = √(k/m), T = 2π/ω
• v = ω√(A² − x²), E = ½kA²
• String v = √(T/μ); open pipe nv/2L; closed pipe (2n−1)v/4L
• Beat frequency f₁ − f₂

Your Study Plan

1. Day 1: SHM kinematics and phase problems.
2. Day 2: spring-mass and pendulum systems including combinations of springs.
3. Day 3: wave equation, string harmonics and organ pipes.
4. Day 4: superposition, beats and timed mixed set.

Practice Oscillations & Waves Questions Free → (opens in a new tab)

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Continue Your Physics Journey

• Previous chapter: Kinetic Theory of Gases
• Next chapter: Electrostatics
• All 20 JEE Main Physics chapters
• Complete JEE Main Syllabus 2027 guide

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Frequently Asked Questions