Reading a Plane-Wave Expression
A harmonic plane wave can be written as A cos(k vector dot r - omega t + phi). Its wave vector points along propagation, its magnitude is the wavenumber, and omega is the angular frequency.
Why this shows up in the exam
Extracting wave speed from a field equation · Finding propagation direction from phase signs · Identifying frequency and wavelength
Learn the idea
The phase of a sinusoidal wave reveals its direction, angular frequency, and wave vector. Follow a point of constant phase. In cos(kx - omega t), keeping the phase fixed requires x to increase with time, so the wave travels in +x; changing the sign before omega t reverses the direction.
🧠 Memory hook: Minus omega t travels with +k.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- phase = k.r - omega t + phi — standard phase for propagation along +k
- v = omega/k — phase speed in a nondispersive medium
- k = 2 pi/lambda, omega = 2 pi f — links phase coefficients to wavelength and frequency
How to approach it
- 1Collect the phase into k.r minus or plus omega t
- 2Read every component of k and calculate its magnitude if needed
- 3Use v = omega/|k| before determining the other field
Common slip-ups that cost marks
- •Reading the field-vector direction as the travel direction
- •Using coefficient k as wavelength
- •Ignoring multiple spatial components of the wave vector
🌟 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.
An electromagnetic wave in vacuum has wavelength 1 m. Take c = 3 x 10^8 m/s. Find its frequency in units of 10^8 Hz.
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