# A Motorcyclist and the Doppler Effect

## The Doppler Effect in Action

**A motorcyclist is moving 24.5 m/s away from a stationary siren, and hears an 894 Hz sound. What is the frequency of the siren when the cyclist is stationary?**

Hint: 894 Hz is the Doppler-shifted frequency

Speed of sound = 343 m/s

Unit = Hz

The frequency of the siren when the motorcyclist is stationary. The frequency of the siren when the motorcyclist is stationary is approximately 822.65 Hz. The frequency of a sound wave changes when either the source of the sound or the observer moves relative to each other. This phenomenon is known as the Doppler effect. In this case, the motorcyclist is moving away from the stationary siren, causing a decrease in the frequency of the sound wave heard by the motorcyclist. To find the frequency of the siren when the cyclist is stationary, we can use the Doppler formula: f' = f(v + vr) / (v + vs) Where f' is the observed frequency, f is the actual frequency of the sound wave, v is the speed of sound, vr is the speed of the motorcyclist, and vs is the speed of the siren. Plugging in the given values: f' = 894 Hz * (343 m/s + 0 m/s) / (343 m/s + 24.5 m/s) f' = 822.65 Hz Therefore, the frequency of the siren when the cyclist is stationary is approximately 822.65 Hz.