An ambulance approaches you while you are stationary. You hear a siren with a frequency of #540#Hz. Once he passes you and is going away from you the frequency is now #440#Hz. How fast was the ambulance going?

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Answer 1 · 2018-02-06T02:50:33

#"32 m/s"#

Let #v# be the speed of sound and #v_s# be the speed of ambulance.

• While approach

#f_"apparent" = f_"original"[v/(v - v_s)]#

#"540 Hz" = f_"original"[v/(v - v_s)]# -----(1)

• When ambulance goes away

#f_"apparent" = f_"original"[v/(v + v_s)]#

#"440 Hz" = f_"original"[v/(v + v_s)]# -------(2)

Divide equations (1) and (2)

#"540 Hz"/"440 Hz" = [(v + v_s)/(v - v_s)]#

#54v - 54v_s = 44v + 44v_s#

#10v = 106v_s#

#v_s = 0.094v#

If speed of sound (#v#) is taken as 340 m/s then speed of ambulance (#v_s#) is 32 m/s.