​ The equation of a simple harmonic progressive wave is given by y = 4 sin π(t/0.02 - x/75). ​

Question

The equation of a simple harmonic progressive wave is given by y = 4 sin π ( \(\frac{t}{0.02}\) - \(\frac{x}{75}\)). Find the displacement and velocity of a particle at 50 cm from the origin and at 0.1 second. (All quantities are expressed in CGS units.)

Answer 1

Data : y = 4 sin \(\pi\)  ( \(\frac{t}{0.02}\) - \(\frac{x}{75}\))

[will all quantities in CGS units],

x= 50 cm, t = 0.1 s

\(\therefore\) y = 4 sin 60\(^\circ\) = 4 \(\frac{\sqrt3}2\) = 2\(\sqrt3\) = 2 x 1.732

= 3.464 cm

The displacement of the particle, y = 3.464 cm = 3.464 × 10^-2 m

The velocity of the particle,