$(27$ points$)$ CH$.12$ An outside stereo speaker at a ski resort emits sound waves with a power output of $86\mathrm{.}00$ W and frequency $1110\mathrm{.}00$ Hz $.$ This problem falls under the topic of a listener moving relative to a stationary source of waves. The speed of sound is assumed to be $v=343\frac{m}{s}.$

A$.(10$ points$)$ Suppose a skier is traveling toward the speaker at speed $22\mathrm{.}01\frac{m}{s}.$ What is the frequency heard by the skier?

B$.(10$ points$)$ Suppose a skier is traveling away from the speaker at speed $18\mathrm{.}03\frac{m}{s}.$ What is the frequency heard by the skier?

C$.(5$ points$)$ Compute the magnitude of the difference in the answers you got for part A and part $B.$

D$.(2$ points$)$ Did you need the power output to solve this problem? Explain.