Understanding the Doppler Effect: A Closer Look at Frequency Changes by an Oncoming Ambulance

The Doppler Effect is a phenomenon observed when the frequency of waves changes for an observer due to motion between the source and the observer. This can be particularly evident when observing vehicles with sirens, such as ambulances moving at significant speeds. In this article, we will explore how an observer experiences the frequency shift when an ambulance emits a steady 800-Hz sound from its siren while moving at 110 km/h, and the changes observed after the ambulance passes.

Scenario and Calculations

Let's consider the scenario where an ambulance moving at 110 km/h emits a constant 800-Hz sound on a day when the speed of sound is 345 m/s. We need to determine the frequency received by an observer watching the oncoming ambulance. The key steps involve converting the speed of the ambulance into meters per second, and then applying the Doppler Effect formula.

Step 1: Convert 110 km/h to m/s

The given speed of the ambulance is 110 km/h. To convert this to meters per second (m/s), we use the conversion factor:

1 km/h 1000 m / 3600 s

110 km/h 110 * (1000 / 3600) m/s 30.56 m/s

Step 2: Apply the Doppler Effect Formula

The formula for the observed frequency (fo) is given by:

(f_{o} f_{s} times frac{v}{v - u})

where:

fs is the source frequency (800 Hz) v is the speed of sound (345 m/s) u is the speed of the source (30.56 m/s)

Substituting the values into the formula, we get:

(f_{o} 800 times frac{345}{345 - 30.56} approx 878 text{ Hz})

After the Ambulance has Passed

Now, let's consider what happens after the ambulance has passed the observer. According to the Doppler Effect, the frequency observed will decrease as the source (the ambulance) moves away from the observer. To reflect this change, we need to add the speed of the ambulance to the denominator in the formula:

(f_{o} f_{s} times frac{v}{v u})

Substituting the values, we get:

(f_{o} 800 times frac{345}{345 30.56} approx 735 text{ Hz})

Conclusion and Learning Outcomes

This example illustrates the Doppler Effect, showcasing how the frequency of sound waves changes based on the motion between a source and an observer. Understanding the Doppler Effect is crucial in various fields, including physics, engineering, and even medicine, where it is used to understand phenomena such as the sound of passing airplanes, starlight shifts, and medical imaging techniques like Doppler ultrasound.

The Doppler Effect is a fascinating area of study that combines the principles of wave mechanics and motion, demonstrating the beauty and complexity of nature. By exploring such phenomena, we can deepen our understanding of the physical world and develop new technologies and applications.

Keywords: Doppler Effect, Sound Waves, Frequency Shift