17.8 Exercise 9

A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency of f, creating a sound wave that moves down the tube. The wave moves through the tube at a speed of $v = 340.00 \text{m}/\text{s} .$ The sound wave is modeled with the wave function $s \left(x , t\right) = s_{\text{max}} \text{cos} \left(k x - \omega t + \phi\right)$. At time $t = 0.00 \text{s}$, an air molecule at $x = 2.3 \text{m}$ is at the maximum displacement of 6.34 nm. At the same time, another molecule at $x = 2.7 \text{m}$ has a displacement of 2.30 nm. What is the wave function of the sound wave, that is, find the wave number, angular frequency, and the initial phase shift?