Asound wave is described by d(y, t)=(0.0200mm)× sin[(8.96rad/m)y+(3140rad/s)t+π/4ra d], where y is in m and t is in s.
in what direction is this wave traveling?
along which axis is the air oscillating?
what is the wavelength?
what is the wave speed?
what is the period of oscillation?

We have a wave function: D(y,t) and we want to know some things about it. 1. The direction the wave is travelling is negative y direction or -y. 2. Since sound waves are longitudinal waves, this sound wave is oscillating along the y axis. 3. The wavelength we can get from k=2π/λ, k is the wave number, λ is the wavelength. So λ=2π/k=6.28/8.96=0.7 m. 4. Before i get the wave speed i will calculate the period of oscillation. It can be calculated from: ω=2πf where ω is angular frequency and f is wave frequency. So f=ω/2π=3140/6.28=500 Hz and the period is T=1/f=1/500=0.002 s. 5. Wave speed is v=λ*f= 0.7*500=350 m/s.