An ambulance has just passed by your home. You detect that the frequency of the receding siren is
900.0 Hz. If you know that the frequency of the ambulance’s siren is 950.0 Hz, how fast is the
ambulance moving? The speed of sound in this case is 335 m/s.
To find the speed of the ambulance, we can use the Doppler effect formula:
\(f' = f \left(\frac{v + v_o}{v + v_s}\right)\)
Where:
- \(f'\) is the observed frequency (900.0 Hz)
- \(f\) is the actual frequency (950.0 Hz)
- \(v\) is the speed of sound (335 m/s)
- \(v_o\) is the velocity of the observer (in this case, the velocity of the person at home)
- \(v_s\) is the velocity of the source (the velocity of the ambulance)
Rearranging the formula to find \(v_s\):
\(v_s = v \left(\frac{f - f'}{f + f'}\right)\)
Substituting the given values:
\(v_s = 335 \left(\frac{950 - 900}{950 + 900}\right) = 335 \left(\frac{50}{1850}\right) \approx 9.0541\) m/s
Therefore, the ambulance is moving at approximately 9.0541 m/s.