Progressive-Wave Equation and Parameters
A one-dimensional harmonic progressive wave is a field y(x,t)=A sin(kx minus-or-plus omega t plus phi), where constant phase points translate with speed omega/k without requiring the medium particles to travel with the wave.
Why this shows up in the exam
Extracting amplitude, wavelength, frequency, phase, and direction · Writing a wave from initial conditions · Comparing particle motion with pattern motion
Learn the idea
A travelling waveform keeps its shape while its phase moves through space at a definite speed. Read a sinusoidal wave as a moving pattern: the coefficient of position fixes wavelength, the coefficient of time fixes frequency, and their signs fix direction.
🧠 Memory hook: Minus with time moves plus in space; plus with time moves minus.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- k = 2pi/lambda, omega = 2pi f — spatial and temporal angular frequencies
- v = omega/k = f lambda — phase speed of a nondispersive harmonic wave
How to approach it
- 1Put the phase in kx plus-or-minus omega t form
- 2Read A, k, omega, and phi with units
- 3Use constant phase to confirm direction and speed
Common slip-ups that cost marks
- •Reading particle velocity as wave velocity
- •Mixing the units of x in a printed equation
- •Inferring direction from k or omega alone
🌟 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.
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