Wave Motion

(1) $φ = {2πx}/{λ}$

(2) $y = a sin(wt – {2πx}/{λ})$
$y = a sin2π (t/T – x/λ)$ … in +ve x – axis

(3) Frequency of beats:
$y_1 = asin 2πn_1 t$
$y_2 = asin 2πn_2 t$
y = R sin2πNt … $N = {n_1 + n_2}/{2}$

(4) Max. Intensity: A = ± 2a
Beat Frequency: $|n_1 – n_2|$
or $n_1 = n_2 ± \text" Beat frequency"$

(5) Doppler Effect:
$n_a = n [{v ± v_o}/{v ± v_s}]$

(6) $φ = {2π(x_2 – x_1)}/{λ}$

(7) Particle velocity:
$v = w √{a^2 – y^2}$