A simple harmonic progressive wave is given by y = y ₀ 2 ( nt - x ) . If the wave velocity is ( 1 8 )^ th the maximum particle velocity then the wavelength is

Step-by-step solution

Given wave equation y = y ₀ ( nt - x ) Particle velocity = dy dt = ( y ₀ n ) ( nt - x ) If the wave velocity is ( 1 8 )^ th of the maximum particle velocity, then, Where is the wavelength and f is the frequency. Frequency is given by f= 2 = n 2 = n 2 Therefore, by plugging f into equation (1), we get the wavelength: = 2 y₀ 8 = y₀ 4