Progressive Wave Equation (y(x,t) = a sin(kx - ωt + φ))

jee-mainjee-advancedneet-ug

y(x,t) = a sin(kx - ωt + φ)

What each symbol means

SymbolWhat it stands for
aAmplitude of wave (m)
kAngular wave number = 2π/λ (rad/m)
φInitial phase (rad)
ωAngular frequency = 2π/T = 2πν (rad/s)
y(x,t)Displacement of medium element at position x and time t
(kx - ωt + φ)Phase of wave

When to use this

Describes sinusoidal wave travelling in +x direction. For wave in -x direction: y = a sin(kx + ωt + φ). Each particle executes SHM with same ω and a but different phase. The function must have x and t in combination (kx ± ωt) to represent a travelling wave. NCERT Eq. 14.2.