The equation of a stationary wave is (all in SI units) y = (0.06) sin (2πx ) cos (5π t ) Match the following…
The equation of a stationary wave is (all in SI units)
y = (0.06) sin (2πx ) cos (5π t )
Match the following columns and mark the correct option from the codes given below.
| Column I | Column II |
| --- | --- |
| (A) Amplitude of constituent wave | (p) 0.06 |
| (B) Position of node at x = K m | (q) 0.5 |
| (C) Position of antinode at x = K m | (r) 0.25 |
| (D) Amplitude at x = 3 m | (s) 0.03 |
(a) s q r p
(b) p r r q
(c) p q r s
(d) p r s q
Solution
General equation for a stationary wave: $y=2A\sin(kx)\cos(\omega t)$.
Comparing with the given equation gives $2A=0.06\Rightarrow A=0.03$.
Positions: nodes at 0.5 m, antinodes at 0.25 m. At $x=3/4$ m amplitude remains $0.06$.
Hence the matches are A→s, B→q, C→r, D→p (option (a)).