Question

Wave in string is represented by :

y(x, t) = 2 sin² (k₁x – w₁t) cos²(k₂x – w₂t).

Numbers of component waves are –

• A. Two
• B. Three
• C. Four
• D. Six

Answer 1

Answer: (C)

Four

Answer 2

y (x, t) = 2 sin² (k₁x – w₁t) cos² (k₂x – w₂t)

= $\frac{1}{2}$ {(1 – cos (2k₁x – 2w₁t)} {1 + cos (2k₂x – 2w₂t)}

= $\frac{1}{2}$ [1 – cos (2k₁x – 2w₁t) – cos (2k₂x – 2w₂t)

+ $\frac{1}{2}$ {cos (2k₁x + 2k₂x – 2w₁t – 2w₂t)} + $\frac{1}{2}$ {cos (2k₁x – 2k₂x – 2w₁t + 2w₂t)]

= $\frac{1}{4}$ [1 – 2 cos (2k₁x – 2w₁t) – 2 cos (2k₂x – 2w₂t) + cos {2(k₁ + k₂) x – 2 (w₁ + w₂) t}

+ cos {2 (k₁ – k₂) x – 2 (w₁ – w₂)t}]