Question

(a) If

y₁ = (2.50 cm)sin

(3.30 cm⁻¹)x − (1.85 s⁻¹)t

and

y₂ = (3.25 cm)sin

(2.25 cm⁻¹)x + (1.25 s⁻¹)t

represent two waves moving toward each other on a string, find the superposition of the two waves at

x = 1.30 cm

and

t = 2.50 s.

cm

(b) Now consider the same two waves on the same string. If they are both moving to the left instead of opposing directions, find the superposition of the waves at

x = 1.30 cm

and

t = 2.50 s.

(Assume the +x direction is to the right.)
cm

Answer 1

a)The super position of two waves is, y=yı + y2 = 2.5 sin (3.3x-1.85t)+3.25 sin (2.25x +1.25t) At t=2.50s and x=1.30cm y = 2.5sin (3.3x – 1.85t)+3.25sin (2.25x+1.25t) = 2.5sin (3.3(1.3)-1.85(2.50))+3.25 sin ( 2.25(1.30)+1.25(2.50)) = 2.5sin(-0.335) +3.25 sin (6.05) =-0.822-0.751 =-1.573cm b)when waves are moving left Now y = y + y2 = 2.5sin (3.3x-1.85t)+3.25(2.25x-1.25t) At t=2.50s and x=1.30cm y = 2.5sin(3.3x –1.85t)+3.25 sin (2.25x-1.25t) 2.5sin (3.3(1.3) – 1.85(2.50))+3.25 sin (2.25(1.30)– 1.25(2.50)) = 2.5sin(-0.335)+3.25 sin (-0.2) =-0.822-0.656 =-1.478cm