Question:
The amplitude of wave disturbance propagating in
the positive $x$-direction is given by $y=\frac{1}{(1+x)^{2}}$ at time $t=0$ and $y=\frac{1}{1+(x-2)^{2}}$ at $t=1 s$, where $x$
and $\mathrm{y}$ are in meres. The shape of wave does not change during the propagation. The velocity of the wave will be______ $\mathrm{m} / \mathrm{s}$.
Solution:
At $t=0, y=\frac{1}{1+x^{2}}$
At time $\mathrm{t}=\mathrm{t}, \mathrm{y}=\frac{1}{1+(\mathrm{x}-\mathrm{vt})^{2}}$
At $\mathrm{t}=1, \mathrm{y}=\frac{1}{1+(\mathrm{x}-\mathrm{v})^{2}} \ldots$ (i)
At $\mathrm{t}=1, \mathrm{y}=\frac{1}{1+(\mathrm{x}-2)^{2}} \ldots$ (ii)
Comparing (i) \& (ii)
$v=2 \mathrm{~m} / \mathrm{s}$
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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