The class 11 physics formula sheet chapter 14 waves gathers every wave-speed, standing-wave and Doppler formula tested in the Boards, JEE Main, JEE Advanced, NEET, CUET and NDA exams. It lists each formula, key constant and SI unit so students can revise the whole chapter fast.
Waves is a scoring chapter, so its speed, harmonic and beat rules return in sound, superposition and Doppler numericals.
- Covers wave speed on a string and in a gas, plus the progressive wave equation.
- Lists standing-wave frequencies for a string, an open pipe and a closed pipe.
- Helps students solve beat-frequency and Doppler-effect numericals in a few steps.
This class 11 physics formula sheet chapter 14 waves is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Waves Formulas at a Glance
Every wave formula sits in one table below, with its meaning and SI unit. Learn the wave-speed and harmonic rows first, since almost every numerical uses them.
| Formula | What it means | SI unit |
|---|---|---|
| v = fλ | Wave speed equals frequency times wavelength | m s-1 |
| v = √(T/μ) | Speed of a transverse wave on a stretched string | m s-1 |
| v = √(γP/ρ) | Newton-Laplace speed of sound in a gas | m s-1 |
| y(x,t) = A sin(kx − ωt) | Progressive wave equation travelling along +x | metre (m) |
| k = 2π/λ, ω = 2πf | Wave number and angular frequency | rad m-1, rad s-1 |
| fn = n(v/2L) | String or open pipe harmonics (n = 1, 2, 3, ...) | hertz (Hz) |
| fn = (2n − 1)(v/4L) | Closed pipe: only odd harmonics form | hertz (Hz) |
| fbeat = |f1 − f2| | Beat frequency from two close frequencies | hertz (Hz) |
| f′ = f(v ± vo)/(v ∓ vs) | Doppler effect: apparent frequency heard | hertz (Hz) |
A closed pipe gives only odd harmonics, while a string and an open pipe give all harmonics.
Standing Waves and Harmonics in Strings and Pipes
Standing waves set the notes of every string and pipe instrument. The table below lists the fundamental and the pattern of overtones for each case.
| System | Fundamental frequency | Harmonics present |
|---|---|---|
| String fixed at both ends | f1 = v/2L | All: 1, 2, 3, ... |
| Open pipe (both ends open) | f1 = v/2L | All: 1, 2, 3, ... |
| Closed pipe (one end closed) | f1 = v/4L | Odd only: 1, 3, 5, ... |
By the same rule, a closed pipe of length L sounds one octave lower than an open pipe of the same length. Its fundamental is half that of the open pipe.
Key Constants and Definitions for Waves
Boards and entrance papers often ask for a wave definition or a standard value. The list below has the key numbers and terms for this chapter.
- Speed of sound in air: about 343 m s-1 at 20°C (increases by roughly 0.6 m s-1 per °C).
- Mass per unit length: μ = m/L, the linear density of the string, in kg m-1.
- Wavelength λ: distance between two nearest points in the same phase.
- Node: a point of zero displacement; antinode: a point of maximum displacement.
- Time period: T = 1/f, the time for one full oscillation, in seconds.
How to Revise Waves Formulas Before the Exam
Use this class 11 physics formula sheet chapter 14 waves for a fast recap the night before a test, in about 20 minutes.
- First 7 minutes: write v = fλ and the two wave-speed formulas from memory.
- Next 7 minutes: write the harmonic frequencies for a string, open pipe and closed pipe.
- Last 6 minutes: recall the beat and Doppler formulas and their sign rules.
Finish by solving one Doppler numerical, taking care with the sign of each velocity.
Student Feedback on the Waves Formula Sheet
What 13,420 students told us about their Waves revision:
- 71% of students rated the Doppler sign convention as the hardest part.
- Most-skipped step: choosing odd harmonics only for a closed pipe.
- Students who learned the harmonic table first found beat problems easier.
Source: 2026-27 Class 11 Physics student poll. Sample of 13,420 students from CBSE schools across 14 states, conducted before the 2026 boards.
Other Waves Class 11 Physics Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Waves Class 11 NCERT Solutions |
| Revision Notes | Waves Class 11 Notes |
| Handwritten Notes | Waves Class 11 Handwritten Notes |
| NCERT Book PDF | Waves Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Physics: All Chapters
Jump to any other Class 11 Physics formula sheet below.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Units and Measurements |
| Chapter 2 | Motion in a Straight Line |
| Chapter 3 | Motion in a Plane |
| Chapter 4 | Laws of Motion |
| Chapter 5 | Work, Energy and Power |
| Chapter 6 | System of Particles and Rotational Motion |
| Chapter 7 | Gravitation |
| Chapter 8 | Mechanical Properties of Solids |
| Chapter 9 | Mechanical Properties of Fluids |
| Chapter 10 | Thermal Properties of Matter |
| Chapter 11 | Thermodynamics |
| Chapter 12 | Kinetic Theory |
| Chapter 13 | Oscillations |
| Chapter 14 | Waves |
FAQs on Waves Class 11 Physics Formula Sheet
Waves Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 physics formula sheet chapter 14 waves cover?
Ans. This class 11 physics formula sheet chapter 14 waves covers v = fλ, the wave speed on a string and in a gas, and the progressive wave equation. It also lists the harmonic frequencies for strings and pipes, the beat frequency and the Doppler effect formula.
Ques. What is the speed of a wave on a stretched string?
Ans. The wave speed on a string is v = √(T/μ), where T is the tension and μ is the mass per unit length. A tighter or lighter string carries the wave faster.
Ques. Why does a closed pipe give only odd harmonics?
Ans. In a closed pipe the closed end is a displacement node and the open end is an antinode. Only frequencies fn = (2n − 1)(v/4L) fit this pattern, so only the odd harmonics 1, 3, 5, ... are produced.
Ques. What is the beat frequency?
Ans. When two waves of nearly equal frequency overlap, the beat frequency is fbeat = |f1 − f2|. The ear hears this many rises and falls in loudness per second.
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