A sound wave travels through a medium with a speed of 320 ~m/s . The distance between two consecutive compressions is 0.4 ~m and the displacement amplitude of the particles in the medium is 2.0 ~mm . The maximum velocity of a particle in the medium is :

Step-by-step solution

The wave speed is v = 320 ~m/s and the wavelength (distance between consecutive compressions) is = 0.4 ~m . The frequency of the wave is given by: f = v = 320 0.4 = 800 ~Hz The angular frequency of the wave is: = 2 f = 2 800 = 1600 ~rad/s The maximum velocity of a particle executing simple harmonic motion in the medium is: v_ max = A Given the displacement amplitude A = 2.0 ~mm = 2.0 10⁻³ ~m , we have: v_ max = (2.0 10⁻³) 1600 = 3.2 ~m/s Answer: 3.2 ~m/s