Answer:
[tex]v_s=27.8m/s[/tex]
Explanation:
If the person hearing the sound is at rest, then the equation for the frequency heard [tex]f[/tex] given the emitted frequency [tex]f_0[/tex], the speed of the truck [tex]v_s[/tex] and the speed of sound [tex]c[/tex] will be:
[tex]f=f_0\frac{c}{c+v_s}[/tex]
Where [tex]v_s[/tex] will be positive if the truck is moving away from the person, and negative otherwise. We then do:
[tex]\frac{f}{f_0}=\frac{c}{c+v_s}[/tex]
[tex]\frac{f_0}{f}=\frac{c+v_s}{c}=1+\frac{v_s}{c}[/tex]
[tex]v_s=c(\frac{f_0}{f}-1)=(340m/s)(\frac{238Hz}{220Hz}-1)=27.8m/s[/tex]
