Physics · Class 11 · Oscillations and Waves

Waves and Sound for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Wave equation, speed of waves on strings and in air, superposition, standing waves, beats and the Doppler effect.

Key ideas

Waves and Sound: what you must understand

y = A sin(kx − ωt) is a wave moving in +x
Standing waves form from two opposite waves; nodes are λ/2 apart
Beats frequency = |f₁ − f₂|
Open pipe: all harmonics; closed pipe: odd harmonics only

Formula sheet

Must-know formulas for Waves and Sound

v = fλ = ω/k
String: v = √(T/μ)
Closed pipe: f = (2n − 1)v / 4L; open pipe: f = nv / 2L
Doppler: f′ = f (v ± v_o)/(v ∓ v_s)

One-page formula sheet

Printable Waves and Sound formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Wrong signs in the Doppler formula
Forgetting end correction when the question gives it
Treating the first overtone as the first harmonic

For the exam

How this topic is asked in JEE

Appears frequently. String and pipe harmonics are asked often. Write the harmonic series before calculating.

Prerequisites: Oscillations (SHM).

NCERT map

Where Waves and Sound is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 11	Physics Part II	Waves	Speed of a Travelling Wave; The Principle of Superposition of Waves; Reflection of Waves; Standing Waves and Normal Modes; Beats; Doppler Effect

JEE Advanced level

A JEE Advanced-level example on Waves and Sound

Question. A string of length 0.5 m is fixed at both ends and vibrates in its fundamental mode at frequency 200 Hz. A tuning fork vibrating at 208 Hz is placed on the opposite side of an observer from the string. Initially the observer is stationary and hears beats. Then the observer starts moving towards the string (and away from the tuning fork) at 8.5 m/s. Take speed of sound in air as 340 m/s. Find (a) the initial beat frequency, and (b) the beat frequency heard by the moving observer.

Show solution

Initial beat frequency = |f_string − f_fork| = |200 − 208| = 8 Hz
When observer moves towards string at v₀ = 8.5 m/s, apparent frequency of string: f'_s = f_s × (v + v₀)/v = 200 × (340 + 8.5)/340 = 200 × 1.025 = 205 Hz
Observer moves away from tuning fork, so apparent frequency of fork: f'_f = f_f × (v − v₀)/v = 208 × (340 − 8.5)/340 = 208 × 0.975 = 202.8 Hz
New beat frequency = |f'_s − f'_f| = |205 − 202.8| = 2.2 Hz

Answer: (a) 8 Hz, (b) 2.2 Hz

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Waves and Sound

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

String Waves (Part-1) | Wave Equation | Wave Speed | PYQs | JEE Physics | Mohit Sir (IIT KGP) — Eduniti - Physics by Mohit Goenka_IITKGP, 35:23
Jump to a subtopic (15)
- 00:00 Introduction
- 00:11 Topics to be discussed
- 01:11 All links for Revision series
- 01:45 Transverse vs Longitudinal Waves
- 03:22 Travelling vs Standing Waves
- 04:12 Wave Equation (on String Waves)
- 07:40 Path and Phase Difference
- 09:02 Direction of Wave Motion Through Equation
- 10:00 Particle Velocity and Acceleration
- 12:51 Particle Direction at time t (2 Methods)
- 15:40 Questions on Wave Equations (PYQs)
- 24:31 Wave Speed on Strings Formulae
- 25:12 Questions on Wave Speed on Strings
- 33:31 Average Power and Intensity Transmitted
- 34:46 PYQs Link
Wave Optics ONE SHOT| Class 12th Physics | JEE Mains & Advance — Lakshya JEE, 1:14:04

Practise

Where to practise for free

2 JEE Main 2026 PYQs on Waves and Sound, with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Waves and Sound important for JEE Main 2027?

Appears frequently. It is part of the official 'Oscillations and Waves' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Waves and Sound?

v = fλ = ω/k; String: v = √(T/μ); Closed pipe: f = (2n − 1)v / 4L; open pipe: f = nv / 2L.

How should I study Waves and Sound for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. String and pipe harmonics are asked often. Write the harmonic series before calculating.