p, q

q, s

r

s, q

Sol. y = 4 sin (5x – 4 t) + 3 cos (4t – 5x + π/6)

is super position of two coherent waves moving in positive direction, so their equivalent will be an another travelling wave.

y = 10 cos sin (100)

lets check at any point, say at x = 0,y = (10 cos t) sin (100 t)

at any point amplitude is changing sinusoidally. so this is equation of beats.

y = 10 sin (2πx – 120t) + 10 cos (120t + 2πx) = superposition of two coherent waves travelling in opposite direction.

⇒ equation of standing waves.

y = 10 sin (2πx – 120 t) + 8 cos (118t – 59/30πx) = superposition of two waves whose frequencies are slightly different (ω 1 = 120, ω 2 = 118)

⇒ equation of Beats.