Answer:
25.5 m/s
Explanation:
The Doppler effect occurs when there is relative motion between a source of a wave and an observer. In such situation, there is a shift in the apparent frequency of the wave perceived by the observer.
The formula that gives the apparent frequency perceived by the observer is:
[tex]f'=\frac{v\pm v_o}{v\pm v_s}f[/tex]
where
f is the real frequency of the wave
f' is the apparent frequency of the wave
v is the speed of the wave
[tex]v_s[/tex] is the velocity of the source (negative if the source is moving towards the observer, positive otherwise)
[tex]v_o[/tex] is the velocity of the observer (positive if the observer is moving towards the source, negative otherwise)
In this problem:
v = 340 m/s is the speed of sound
f = 800 Hz is the frequency of the horn
f' = 860 Hz is the apparent frequency
[tex]v_o=0[/tex] (the observer is at rest)
Re-arranging the equation for [tex]v_s[/tex], we can find the velocity of the horn and the driver:
[tex]f'=\frac{v}{v-v_s}f\\(v-v_s)f'=vf\\vf'-v_sf'=vf\\v_s=v\frac{f'-f}{f'}=(340)\frac{860-800}{860}=25.5 m/s[/tex]
So, 25.5 m/s towards the observer.
