The principle of superposition of waves states that when two or more waves overlap in the same medium, the resultant displacement at any point is the algebraic sum of the displacements due to each wave at that point. This principle explains interference, diffraction, and formation of standing waves.
Waves - Definition, Types, Properties, Application
When a pebble is dropped into still water, ripples spread outward in circles, creating the illusion that water is moving yet the cork pieces on the surface only bob up and down. This shows that waves transfer energy, not matter. Similarly, when we speak, sound waves travel through air without moving the air itself. Waves are simply patterns of disturbance that carry energy and information, and the chapter on Waves is very important for your school exams as well as for competitive exams like JEE and NEET.
1. Introduction
When a small disturbance is created in a medium, it does not stay at one point but travels outward as a wave. For example, dropping a pebble in water produces ripples that move outwards, though the water itself does not flow away only the disturbance moves. Similarly, when we speak, sound waves travel in air without the bulk movement of air. Waves are, therefore, disturbances that transfer energy and information from one place to another without the actual transfer of matter. They play a vital role in communication, carrying signals in the form of sound, electrical, or electromagnetic waves.
2. Transverse and Longitudinal Waves
In a transverse wave, particles of the medium oscillate perpendicular to the direction of wave propagation (e.g., waves on a string, light waves).
In a longitudinal wave, particles oscillate parallel to the direction of wave propagation (e.g., sound waves in air).
3. Displacement Relation in a Progressive Wave
A progressive wave is represented as:
For a wave travelling in the $\mathbf{+ x}$ direction:
$
y(x, t)=A \sin (k x-\omega t+\phi)
$
For a wave travelling in the -x direction:
$
y(x, t)=A \sin (k x+\omega t+\phi)
$
4. The Speed of a Travelling Wave
The speed of a travelling wave depends on the properties of the medium in which it moves. For a string under tension, the wave speed is given by
$
v=\sqrt{\frac{T}{\mu}}
$
where $T$ is the tension in the string and $\mu$ is the mass per unit length. In general, wave speed is determined by how quickly disturbances are transmitted through the medium.
5. The Principle of Superposition of Waves
6. Reflection of Waves
When a wave strikes a boundary or obstacle, it bounces back into the same medium. This phenomenon is called reflection of waves. The nature of reflection depends on the type of boundary:
At a fixed boundary, the wave is reflected with a phase change of π (inverted).
At a free boundary, the wave is reflected without phase change.
7. Beats
Beats are the periodic variations in sound intensity that occur when two sound waves of slightly different frequencies interfere.
- The waves alternately reinforce (constructive interference) and cancel each other (destructive interference).
- The number of beats heard per second is equal to the difference in frequencies of the two sources:
$
\text { Beat frequency }=\left|f_1-f_2\right|
$
Waves Class 11th Important Formula
1. Displacement relation of a progressive wave:
$
y(x, t)=A \sin (k x-\omega t+\phi)
$
2. Wave speed (string):
$
v=\sqrt{\frac{T}{\mu}}
$
where $T=$ tension, $\mu=$ mass per unit length.
3. Wave speed (sound in medium):
$
v=\sqrt{\frac{\gamma P}{\rho}}=\sqrt{\frac{\gamma R T}{M}}
$
4. Wavelength-frequency relation:
$
v=\lambda f
$
5. Principle of superposition:
$
y=y_1+y_2
$
6. Beat frequency:
$
f_{\text {beat }}=\left|f_1-f_2\right|
$
Exam-wise Weightage of Waves
| Exam | Approximate Weightage | Remarks |
|---|---|---|
| NEET | 1 Question | Usually 1 question, often from beats, resonance, or speed of sound. |
| JEE | 1 Question | 1 questions, mainly from standing waves, organ pipes, or superposition. |
Waves Real Life Example
- Sound Waves in Music & Communication – Musical instruments (guitar, flute, tabla) produce sound due to vibrating strings or air columns; human speech and hearing also rely on sound waves.
- Medical Uses (Ultrasound) – Ultrasound waves are used in medical imaging (sonography) and to break kidney stones.
- Seismic Waves – Earthquakes produce seismic waves, which help scientists study the Earth’s interior.
- Communication Systems – Radio, TV, and mobile phones use electromagnetic waves for transmitting signals.
NEET Highest Scoring Chapters & Topics
This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.
Download E-bookRelated Topics,
Important concepts and Laws
- Waves
- Characteristics of waves.
- Mechanical waves.
- Electromagnetic Waves.
- Matter waves.
- Transverse wave motion.
- Longitudinal wave motion.
- Wavelength and Frequency.
- Wave Velocity.
- Amplitude.
- Time Period.
- Relation between phase and path difference.
- The Principle of Superposition of Wave.
- Standing waves or Stationary waves.
- Frequency of the Stretched String.
- Beats.
- Doppler Effect.
NCERT Notes Subject Wise Link:
- NCERT notes Class 11 Maths
- NCERT notes Class 11 Physics
- NCERT notes Class 11 Chemistry
- NCERT notes Class 11 Biology
NCERT Solutions Subject wise link:
- NCERT solutions for class 11 Physics.
- NCERT solutions for class 11 Chemistry.
- NCERT solutions for class 11 Mathematics.
- NCERT solutions for class 11 Biology.
NCERT Exemplar Solutions Subject wise link:
Frequently Asked Questions (FAQs)
Q: Earth does not hear explosions on other worlds. Why?
A:
Earth does not hear explosions on other planets because there is no material medium between the earth and the planets over a long distance, and sound waves cannot propagate without a material medium.
Q: Why are pressure waves termed longitudinal waves?
A:
Longitudinal waves are called pressure waves because the propagation of longitudinal waves in a medium involves fluctuations in air volume and pressure, which result in compressions and rarefactions.
Q: What is the purpose of the two prongs on tuning forks?
A:
A tuning fork has two prongs because the two prongs produce resonance vibrations that make the vibrations last longer.
Q: On an overcast day, sound velocity increases. Why?
A:
On a cloudy day, sound velocity increases because the air is wet and contains a lot of moisture, the density of air is reduced, and because velocity is inversely related to density, sound velocity increases.
Q: Is it possible to make beats with two light sources with roughly similar frequencies?
A:
No, because light emission is a random and quick occurrence, and instead of beats, we get uniform intensity.
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Correct Answer: Only 1,2 , and 4
Solution : The correcrt option is 4 i.e "Only 1, 2, and 4."
Explanation:
Let's refer to the following lines of the passage:
The device has a very simple structure consisting of specially designed nanocomposite polymers and contact electrodes and can generate a few Milliwatt (Mw) power, which is sufficient to power small electronic devices like watches, digital thermometers, radio frequency transmitters, healthcare sensors, pedometers.
The above statement clearly mention the watches, pedometers and radio frequency transmitters.
Correct Answer: response
Solution : The second option is the correct choice.
The sentence discusses the need to mitigate the effects of climatic disasters, investing in disaster preparedness, and the specific types of actions required. Response is the most fitting term because it implies taking action to address and manage the impact of climatic disasters effectively.
The meanings of the other options are as follows:
- Regeneration: the process of renewal, restoration, or growth.
- Evaluation: the act of assessing or appraising the effectiveness or value of something.
- Manifestation: the display or demonstration of a particular quality, emotion, or phenomenon.
Therefore, the complete sentence is: "To mitigate the effects of these disasters, it is essential to invest in disaster preparedness and response."
Correct Answer: frequent
Solution : The third option is the correct choice.
The context of the sentence discusses the consequences of rising temperatures, indicating an increase in the occurrence of droughts and floods. The term "frequent" appropriately conveys the idea of these events happening more often.
The meanings of the other options are as follows:
- Fast: Quick or rapid.
- Rare: Uncommon or infrequent.
- Speedy: Fast or quick.
Therefore, the complete sentence is: "Rising temperatures can lead to more frequent heat waves, while changes in precipitation patterns can lead to more frequent droughts and floods."
Correct Answer: Either longitudinal or transverse
Solution : The correct option is Either longitudinal or transverse.
In solids, sound can travel as both longitudinal waves and transverse waves. Longitudinal sound waves involve oscillations of pressure deviations from the baseline pressure, creating regions of compression, and rarefaction. Meanwhile, transverse waves in solids consist of alternating shear stress occurring perpendicular to the direction of propagation.