A transverse harmonic wave on a string is y(x,t) = 5 sin(6t + 0.003x), where x and y are in cm and t is in seconds. The wave speed is ______ m s⁻¹.
Physics · Circular Motion
JEE Mains 10 April 2023 Shift 1 Morning Shift

Question

A transverse harmonic wave on a string is y(x,t) = 5 sin(6t + 0.003x), where x and y are in cm and t is in seconds. The wave speed is ______ m s⁻¹.

G1 Physics · Accepted Answer

Compare the wave with y = A sin(ωt + kx) Here, ω = 6 rad s⁻¹ The coefficient of x is 0.003 per cm. Converting to per metre: k = 0.003 × 100 = 0.3 rad m⁻¹ Wave speed: v = ω/k = 6/0.3 = 20 m s⁻¹ Final value: 20