IIT JEE Physics Practice Paper – Waves (Set 24)
Instructions
Total Questions: 20 | Marks: 4 each | No Negative Marking
Waves – IIT JEE Notes (Set 24)
Introduction to Waves
Definition
A wave is a disturbance that transfers energy from one place to another without transfer of matter.
Main Concept
Particles of medium oscillate about their mean positions while energy propagates through the medium.
Characteristics of Waves
Amplitude
Maximum displacement of particle from mean position.
Wavelength
Distance between two consecutive points in same phase, such as two crests or troughs.
Frequency
Number of oscillations completed in one second.
Time Period
Time taken to complete one oscillation.
Wave Speed
Distance traveled by wave per unit time.
Wave Equation
v = fλ
Types of Waves
Mechanical Waves
Require material medium for propagation.
Examples
Sound waves, water waves, waves on string.
Electromagnetic Waves
Do not require any material medium and can travel through vacuum.
Examples
Light waves, radio waves, X-rays.
Transverse Waves
Definition
Particles of medium vibrate perpendicular to direction of wave propagation.
Examples
Light waves and waves on stretched string.
Important Feature
Contain crests and troughs.
Longitudinal Waves
Definition
Particles of medium vibrate parallel to direction of propagation.
Examples
Sound waves in air.
Important Feature
Contain compressions and rarefactions.
Wave Motion
Energy Transfer
Waves transfer energy without transporting matter permanently.
Particle Motion
Particles oscillate around equilibrium positions.
Speed of Mechanical Waves
String Wave Speed
v = √(T/μ)
Variables
T = tension in string
μ = mass per unit length
Key Insight
Wave speed increases with tension.
Sound Waves
Nature
Sound waves are longitudinal mechanical waves.
Requirement
Sound requires material medium for propagation.
Speed of Sound
Depends on elasticity and density of medium.
Speed of Sound in Air
Formula
v = √(γP/ρ)
Temperature Dependence
Speed of sound increases with temperature.
Humidity Effect
Sound travels faster in humid air.
Audible Sound Range
Human Hearing Range
20 Hz to 20 kHz.
Infrasonic Waves
Frequency below 20 Hz.
Ultrasonic Waves
Frequency above 20 kHz.
Applications of Ultrasonic Waves
Medical Use
Ultrasound imaging and therapy.
Industrial Use
Crack detection and cleaning.
SONAR
Used for underwater detection and distance measurement.
Principle of Superposition
Definition
Resultant displacement equals algebraic sum of individual displacements.
Importance
Explains interference and stationary waves.
Interference of Waves
Constructive Interference
Occurs when waves combine in same phase and amplitude increases.
Destructive Interference
Occurs when waves combine in opposite phase and amplitude decreases.
Beats
Definition
Periodic variation in intensity due to superposition of two waves of nearly equal frequencies.
Beat Frequency
f = |f₁ – f₂|
Application
Tuning musical instruments.
Stationary Waves
Definition
Produced due to superposition of two identical waves traveling in opposite directions.
Nodes
Points having zero displacement.
Antinodes
Points having maximum displacement.
Formation of Standing Waves on Strings
Fundamental Mode
Lowest frequency mode of vibration.
Harmonics
Integral multiples of fundamental frequency.
Resonance
Definition
Maximum amplitude occurs when driving frequency equals natural frequency.
Examples
Musical instruments and bridges.
Doppler Effect
Definition
Apparent change in frequency due to relative motion between source and observer.
Approaching Source
Frequency appears higher.
Receding Source
Frequency appears lower.
Intensity of Waves
Definition
Energy crossing unit area per second.
Relation
Intensity ∝ Amplitude²
Wave Number
Definition
Number of waves per unit distance.
Formula
k = 1/λ
Phase of a Wave
Definition
Specifies state of oscillation of particle at any instant.
Phase Difference
Difference in phase between two particles.
Energy in Wave Motion
Kinetic Energy
Due to motion of particles.
Potential Energy
Due to elastic deformation of medium.
Total Energy
Remains conserved in ideal wave motion.
Conceptual Insights
Key Understanding
Wave motion transfers energy while particles only oscillate around equilibrium positions.
Common Mistakes
Students often confuse longitudinal and transverse waves and mix up nodes with antinodes.
Important Exam Concepts
Conceptual Traps
Sound waves cannot travel through vacuum because they require material medium.
JEE Strategy
Practice wave equations, Doppler effect numericals, stationary wave problems, and concepts of resonance thoroughly.