A transverse wave on a string is y = 0.02 sin(2πx−10πt) in SI units. At x = 0 and t = 0, the magnitude of transverse particle velocity is Nπ/10 m/s. Find N.
Physics · Wave Motion · general equation of wave
JEE Mains NEET JEE Advanced

Question

A transverse wave on a string is y = 0.02 sin(2πx−10πt) in SI units. At x = 0 and t = 0, the magnitude of transverse particle velocity is Nπ/10 m/s. Find N.

G1 Physics · Accepted Answer

Particle velocity is uᵧ = ∂y/∂t = −0.02(10π)cos(2πx−10πt). At x = 0, t = 0, cos0 = 1. Therefore, |uᵧ| = 0.2π m/s = 2π/10 m/s. Hence, N = 2.