To solve this problem it is necessary to apply the concepts related to Dopler's Law. Dopler describes the change in frequency of a wave in relation to that of an observer who is in motion relative to the Source of the Wave.
It can be described as
[tex]f = \frac{c\pm v_r}{c\pm v_s}f_0[/tex]
c = Propagation speed of waves in the medium
[tex]v_r[/tex]= Speed of the receiver relative to the medium
[tex]v_s[/tex]= Speed of the source relative to the medium
[tex]f_0 =[/tex]Frequency emited by the source
The sign depends on whether the receiver or the source approach or move away from each other.
Our values are given by,
[tex]v_s = 32.2m/s \rightarrow[/tex] Velocity of car
[tex]v_r = 14.8 m/s \rightarrow[/tex] velocity of motor
[tex]c = 343m/s \rightarrow[/tex] Velocity of sound
[tex]f_0 = 523Hz \rightarrow[/tex]Frequency emited by the source
Replacing we have that
[tex]f = \frac{c + v_r}{c - v_s}f_0[/tex]
[tex]f = \frac{343 + 14.8}{343 - 32}(523)[/tex]
[tex]f = 601.7Hz[/tex]
Therefore the frequency that hear the motorcyclist is 601.7Hz
