Wave Pulses and Kinematic Translation
Any differentiable pulse y(x,t)=F(x minus vt) is a right-moving solution and y(x,t)=F(x plus vt) is a left-moving solution of the one-dimensional wave equation in a uniform nondispersive medium.
Why this shows up in the exam
Reading rational or Gaussian pulse equations · Locating a pulse after a time interval · Relating pulse width to spatial shape
Learn the idea
A pulse moves by translating its shape, so its argument reveals speed and direction directly. Imagine sliding the entire graph without stretching it: a function of x minus vt moves right, while a function of x plus vt moves left.
🧠 Memory hook: Freeze the argument: x minus vt goes right.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- y = F(x - vt) — unchanged pulse translating in the positive x direction
- y = F(x + vt) — unchanged pulse translating in the negative x direction
How to approach it
- 1Set the pulse argument equal to a constant
- 2Solve for dx/dt to get direction and speed
- 3Read amplitude and symmetry from the shape function
Common slip-ups that cost marks
- •Treating the sign of displacement as direction
- •Differentiating before identifying the translated coordinate
- •Calling pulse width a wavelength
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
More from Oscillations and Waves
Superposition, Beats, and Resonance
Explore the principles of superposition, formation of beats, beat frequency, resonance, and phase difference in wave phenomena.
Standing Waves and Harmonics
Understand the formation of standing waves, harmonics in strings and organ pipes (open and closed), and the relationship between displacement and pressure in stationary waves.
Velocity and Acceleration in SHM
Explore how velocity and acceleration vary with displacement and time in SHM, including maximum values and their physical significance.
Simple Pendulum and Spring Systems
Study the time period formulas, energy considerations, and behavior of simple pendulums and spring-mass systems, including effects of non-inertial frames and spring combinations.
Basics of Simple Harmonic Motion (SHM)
Understand the defining features of SHM, including its standard equations, conditions, and the relationship between displacement, velocity, and acceleration.
Wave Motion and Wave Equation
Learn the fundamentals of wave motion, including the wave equation, its parameters, direction, and the distinction between particle and wave velocities.