A fire station has a horn that sounds a 1750Hz. If you are on your bike moving toward it at 8m/s, what will be the frequency you hear? Assume the air is 20 degrees Celsius.
Since you are moving toward the source of the sound, the frequency of the sound will be shifted according to the formula [tex]f'= \frac{v+v_o}{v} f[/tex] where v is the speed of sound (343 m/s) [tex]v_o[/tex] is the speed of the observer relative to the source, and it is positive when the observer is moving towards the sound (so in this case, [tex]v_o=8 m/s[/tex]) f=1750 Hz is the original frequency of the sound
Plugging the numbers into the equation, we find that the frequency you will hear is [tex]f'= \frac{343 m/s+8m/s}{343 m/s} (1750 Hz)=1791 Hz [/tex]
