Beats: Definition, Class 11 Physics Notes, Working Principle, Beat Frequency Formula

Physics Waves 2025

Syed Aquib Ur Rahman
Updated on Aug 4, 2025 19:12 IST

By Syed Aquib Ur Rahman, Assistant Manager

In Class 11’s Physics chapter on Waves, you learn about fundamental wave properties, how to represent them mathematically, and the important principle of superposition. Once these are clear, you land on the last section - Beats. It’s a pretty interesting concept, especially when you enjoy listening to or playing music. 

Most people think ‘beats’ are rhythms in a song. But here, you’re learning deeper in how sound waves combine to create those rhythmic rises and falls in loudness. 

We will define Beats in Physics in detail below. Right from examples of beats to the beat frequency formula, we have you covered.

Beats in Physics
Table of content
  • What are Beats?
  • Why Learn Beats in Physics for Exams
  • How NCERT Defines Beats in Physics
  • Working Principle of Beats in Physics
  • Difference Between Beats and Standing Waves
  • Beats in Physics: Use of Pressure Equation and Trigonometric Identity
  • Beats Frequency Formula and Derivation
  • Real-Life Examples of Beats in Physics
  • Revision Notes for Physics Class 11
  • NCERT Solutions for Physics Class 11 to Practice
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What are Beats?

Beats happen when two different sounds at slightly different frequencies play together. When you notice it closely, it’s a pulsing effect. Here, the sound gets louder and softer again and again. So, when you visualise, this sound appears like a wave, with the louder part appearing like a crest while the softer part is the trough. Now, this up and down movement in volume (or intensity or amplitude) caused by close frequencies is a beat in physics.

 

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Why Learn Beats in Physics for Exams

So, when appearing for JEE Mains or similar exams, your knowledge of Beats in terms of wave mechanics is pretty important. Here are some aspects you could consider beyond the beats definition in physics. The entrance exam questions usually revolve around the following areas. 

  • Learn the mathematical derivation of the beat equation, and how the phase difference between interfering waves creates a beat. 
  • Understand how beats are connected to other wave phenomena, as there are integrated questions in engineering entrances. 
  • Practice solving numerical problems; questions may come on finding variations in amplitude in the resulting wave from interfering waves. 
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How NCERT Defines Beats in Physics

In Section 14.7 of the Waves chapter, NCERT defines beats as

‘Beats’ is an interesting phenomenon arising from interference of waves. When two harmonic sound waves of close (but not equal) frequencies are heard at the same time, we hear a sound of similar frequency (the average of two close frequencies), but we hear something else also. We hear audibly distinct waxing and waning of the intensity of the sound, with a frequency equal to the difference in the two close frequencies.

To really understand how beats work as waves, a few sound concepts are in your NCERT textbook, and they are explained with equations.

Don’t get overwhelmed, here are the basics you can always refer to before approaching any equation and further beats related concepts in physics in this section of the chapter. 

Terminology of Beats in Physics

  • Waxing and Waning - Waxing is the crest or rise in the sound wave, while waning is the trough or fall. 
  • Superposition is the main rule of how two travelling waves combine or sum themselves to create the pulsing effect we now know as beats. 
  • Acoustics - It’s the study of sound. 
  • Harmonic Sound Waves - Harmonic sounds have regular patterns where waves repeat smoothly, and the frequencies are in whole numbers, such as 100 Hz, 200 Hz, and so on. 
  • Amplitude - Beats sound high and low in volume when the amplitude of the waves keeps changing. 
  • Angular Frequency - It’s the difference in speed of the two waves that causes the beat pattern. 

 

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Working Principle of Beats in Physics

Let's find out how beats work in physics. 

Frequencies are Never Identical 

Beats require two similar frequencies, but they should never be identical. 

They will have the same phase if they are identical or have the same frequency. That means the waves with the same frequencies will either add up, causing constant loudness, or cancel out, causing no sound. 

Repeating Pattern in Same Direction and Amplitude

The close frequencies that cause beats need to travel in the same direction. It is the simple principle that tells us that beats are a time-based effect

The reasoning is that two waves causing a beat must arrive at some point from the same direction, and at nearly the same time. Only then can these two waves interfere correctly. 

Also, the two waves must have the same volume. It is hard to understand what causes the pulsation if one is too faint to hear. 

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Difference Between Beats and Standing Waves

Before diving into the mathematical side of beats in physics, let's remove some misconceptions you may have with similar but not the same interference phenomena, beats and standing waves. 

Feature Beats Standing Waves
Origin Superposition of two sound waves of slightly different frequencies Superposition of two identical waves travelling in opposite directions, caused by the reflection of waves
Observable Pattern Loud and soft oscillations, heard at a single point over a defined period Fixed nodes and antinodes along the medium
Dependence on Direction Both waves travel in the same direction Waves travel in opposite directions (reflection at boundaries)
What Changes Amplitude varies in time Amplitude varies in space
Practical Example Tuning musical instruments Standing waves on a stringed instrument, air columns in pipes
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Beats in Physics: Use of Pressure Equation and Trigonometric Identity

Before going further to understand the beats in physics formula, let’s look into two aspects. 

Sound pushes and pulls air particles, which makes it a longitudinal wave. We can measure sound as a wave by looking at how air pressure changes in time and space, just because we know that a longitudinal wave's speed depends on the elastic property and density. 

Why we use the pressure equation in beats

We can model the pressure as a sine wave. This is the ideal way to apply physics and maths tools and predict the interaction of sound waves. 

p = p 0 sin ( ω t ) Why we also use a trigonometric identity

Adding two sine functions could become complicated when we want to find out more about beats, and not just how sound waves interact. We could also find out how fast the wave oscillates, and how the amplitude or volume changes over time, here. That’s where a trigonometric identity comes in.

Let’s see how we can calculate beats, considering these conditions. Based on that, we will be able to understand what beat frequency is.  

 

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Beats Frequency Formula and Derivation

Beats in physics are formed by wave superposition. We can figure that out mathematically, by

Starting with Two Waves

Here we will consider two sound waves. They meet certain conditions. 

  • They move in the same direction
  • Their amplitudes are the same, with slightly different frequencies

The pressure equation then is

p 1 = p 0 sin [ ω 1 ( t x v ) ]

p 2 = p 0 sin [ ω 2 ( t x v ) ]

P0 is the maximum pressure

w1 and w2 are angular frequencies of the two waves

x is the position

t is the time

v is the velocity or speed of sound

Adding Two Waves

Let’s recap the concept of superposition here. 

The superposition principle in the context of waves is that, 

When waves are moving at the same time in the same direction, the total effect is just the sum of each individual wave. 

So when two waves meet, we write the equation based on the superposition principle in this way. 

p = p 1 + p 2 = p 0 [ sin ( ω 1 ( t x v ) ) + sin ( ω 2 ( t x v ) ) ]

Now that we know the reason for learning about using a trigonometric identity, here is how we can show it, while using the superposition principle.

sin A + sin B = 2 cos ( A B 2 ) sin ( A + B 2 )

To apply this principle, 

p = 2 p 0 cos ( ω 1 - ω 2 2 ( t - x v ) ) sin ( ω 1 + ω 2 2 ( t - x v ) ) Let 
Δ ω = ω 1 - ω 2 ω = ω 1 + ω 2 2 Then, what we have is 
p = A sin [ ω ( t - x v ) ] , where A = 2 p 0 cos ( Δ ω 2 ( t - x v ) )

 

Meaning of the Beats Equation

The final wave looks as it is a regular wave with a frequency, ω. Only that, the amplitude keeps changing. The sound keeps getting louder and softer. 

Deriving the Beats Frequency Equation

We know

A = 2 p 0 cos ( Δ ω 2 ( t - x v ) ) This amplitude varies slowly.

Now, the rate at which the amplitude goes from maximum to minimum is called the beat frequency

So, if, 

ω 1 = 2 π ν 1 ω 2 = 2 π ν 2 The beat frequency becomes
f beats = | ν 1 - ν 2 |

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Real-Life Examples of Beats in Physics

Let's look into some core examples of beats in physics, observed in the real world.  

Tuning Musical Instruments

As it’s obvious, musicians listen for beats when tuning a piano, guitar, or any other instrument. They listen for beats between two strings. If there are slow pulsations, there could be slight frequency mismatches. When there is no beat, they can confirm perfect tuning.

Audio Technology

Sound engineers use beat frequencies in introducing phasing and chorus effects. Such layering of close-frequency signals creates rich, dynamic textures, and they are spread across the stereo field to engulf the listener in an immersive experience.  

Other Uses

In medicine, ultrasonic beat waves help in imaging contrast. That can modulate tissue vibrations for targeted therapies.

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Revision Notes for Physics Class 11

Find all the important links for in-depth and easy-to-understand notes on the following Physics chapters in your NCERT syllabus that we regularly update. 

Units and Measurements Class 11 Notes Mechanical Properties of Solids Class 11 Notes
Motion in a Straight Line Class 11 Notes Mechanical Properties of Fluids Class 11 Notes
NCERT Class 11 Notes for Motion in a Plane Thermal Properties of Matter Class 11 Notes
Laws of Motion Class 11 Notes Thermodynamics Class 11 Notes
Work, Energy, and Power Class 11 Notes Kinetic Theory of Gas Class 11 Notes
System of Particles and Rotational Motion Class 11 Notes Oscillations Class 11 Notes
Gravitation Class 11 Notes Waves Class 11 Notes

Get an overview of all core subjects in the Science stream below.

NCERT Class 11 Notes for PCM
NCERT Class 11 Physics Notes

 

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NCERT Solutions for Physics Class 11 to Practice

Q&A Icon
Commonly asked questions
Q:  

What is the frequency of a beat?

A: 

Beat frequency is the rate of amplitude modulation we hear when two wave frequencies, f1 and f2 interfere. It's given by |f1-f2|. It represents how fast the loudness oscillates over time. 

Q:  

What are conditions for beat frequency?

A: 

Beats form when two harmonic waves of nearly equal frequencies and identical amplitudes travel in the same direction, whic allows the superposition of waves. 

Q:  

What causes a beat wave?

A: 

A beat wave arises due to constructive and destructive interference between two sound waves. These two frequencies have nearly equal frequencies but never the same. The resulting amplitude envelope oscillates at the beat frequency.  

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