A travelling sound wave is described by the equation y = 6.0 (600 t - 1.8 x) , with y measured in 10⁻⁵ m , t in second, and x in metre. Determine the ratio of the velocity amplitude of the particles to the wave speed.

Step-by-step solution

The given equation of the wave is y = 6.0 10⁻⁵ (600 t - 1.8 x) . Comparing with the standard wave equation y = A ( t - k x) , we get: A = 6.0 10⁻⁵ m = 600 rad/s k = 1.8 m ⁻¹ The velocity amplitude of the particles is given by v_m = A . The wave speed is given by v = k . The ratio of the velocity amplitude of the particles to the wave speed is: Ratio = v_m v = A / k = A k Substituting the values: Ratio = (6.0 10⁻⁵) 1.8 = 10.8 10⁻⁵ = 1.08 10⁻⁴ 1.1 10⁻⁴