Question

A wave travelling along a string is described by, y(x, t) = 0.005 sin (80.0 x – 3.0 t), in which the numerical constants are in SI units (0.005 m, 80.0 rad m^–1, and 3.0 rad s^–1). Calculate the displacement y of the wave at a distance x = 30.0 cm and time t = 20 s?
1. 7 mm
2. 3 mm
3. - 3 mm
4. 5 mm

Answer 1

Correct Answer - Option 4 : 5 mm

The displacement y at x = 30.0 cm and time t = 20 s is given by

y = (0.005 m) sin (80.0 × 0.3 - 3.0 × 20) = (0.005 m) sin (-36)

As sin (2nπ + θ) = sin θ and 12π > 36

= (0.005 m) sin (-36 + 12π)

= (0.005 m) sin (1.699)

As 1 radian = 180°/π ⇒ 1.699 rad = 1.699 × 180°/π = 97°

(It can be approximated as : sin90° ≈ 1)

= (0.005 m) sin (97⁰) ≈ 5 mm