Question

One day when the speed of sound in air is 343 m/s, a fire truck traveling at vs = 29 m/s has a siren which produces a frequency of fs = 401 hz. vs = 29 m/s f = 401 hz what frequency, in units of hertz, does the driver of the truck hear?

Answer 1

The observed frequency of the ambulance siren is lower than the actual frequency due to the Doppler effect. By using the formula for the Doppler effect, the speed of the ambulance can be calculated to be approximately 9.48 m/s.

Step-by-step explanation:

Frequency and the Doppler Effect

The frequency of a sound wave is affected by the motion of the source of the sound and the motion of the observer. This is known as the Doppler effect. When the source of the sound is moving towards the observer, the observed frequency is higher than the actual frequency. Conversely, when the source is moving away from the observer, the observed frequency is lower than the actual frequency.

In the given question, the observer is stationary and the ambulance is moving away. The observed frequency is 101 Hz, which is lower than the actual frequency of 105 Hz. To find the speed of the ambulance, we can use the formula:

observed frequency / actual frequency = (speed of sound + speed of observer) / (speed of sound - speed of source)

Substituting the given values, we have:

101 Hz / 105 Hz = (331 m/s + 0 m/s) / (331 m/s - speed of ambulance)

Solving for the speed of the ambulance, we find that it is approximately 9.48 m/s.