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 displacement amplitude of the particles to the wavelength of the wave.

Step-by-step solution

The given equation of the travelling sound wave is y = 6.0 (600 t - 1.8 x) . Comparing this with the standard wave equation y = A ( t - k x) , we get: Displacement amplitude, A = 6.0 10⁻⁵ m Angular wave number, k = 1.8 rad/m The wavelength of the wave is given by: = 2 k = 2 1.8 = 0.9 m The ratio of the displacement amplitude to the wavelength is: A = 6.0 10⁻⁵ 0.9 = 5.4 10⁻⁵ Using 3.14 , we get: A = 5.4 10⁻⁵ 3.14 1.7 10⁻⁵