Question

A police siren contains at least two frequencies, producing the wavering sound (beats). Explain how the siren sound changes as a police car approaches, passes, and moves away from a pedestrian.

Short answer

Answer: As a police car approaches a pedestrian, the siren's frequency increases, making it sound higher-pitched due to the Doppler effect, and the beat frequency also increases. While the police car passes by the pedestrian, the siren's frequency remains constant momentarily, as does the beat frequency. As the car moves away from the pedestrian, the siren's frequency decreases, making it sound lower-pitched due to the Doppler effect, and the beat frequency decreases as well.

Step-by-step solution

Understanding beat frequency and Doppler effect

First, we should understand the phenomena of beat frequency and the Doppler effect. Beat frequency is the pulsating sound one hears when two similar frequencies combine. In this case, the two frequencies are produced by the police siren. The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. In the context of our exercise, the Doppler effect describes how the frequency of the police siren changes as the car approaches and moves away from the pedestrian.

Siren as the police car approaches

When the police car is approaching a pedestrian, due to the Doppler effect, the frequency of the siren heard by the pedestrian increases. This means that the police car's siren sounds higher-pitched than when the car is stationary. During this time, the beat frequency will also increase as the difference between the two siren frequencies becomes larger.

Siren as the police car passes by

As the police car passes by the pedestrian, the siren sound's frequency remains constant for a very brief moment. At this point, the pedestrian hears the actual siren frequencies without any modification due to the Doppler effect. The beat frequency remains constant in this moment.

Siren as the police car moves away

When the police car begins to move away from the pedestrian, the Doppler effect causes the siren's frequency to decrease in the ears of the pedestrian. The siren will now sound lower-pitched than when the car was stationary. The beat frequency will also decrease as the difference between the two siren frequencies becomes smaller. In summary, as the police car approaches, passes, and moves away from a pedestrian, the sound of the siren changes primarily due to the Doppler effect altering the frequency of the siren. The change in beat frequency is also directly related to the Doppler effect as the difference between the two siren frequencies increases and decreases.

Key concepts

Beat Frequency

When you listen closely to a police siren, you might notice it produces a fluctuating sound. This fluctuation is created by the beat frequency. Simply put, beat frequency occurs when two sound waves of slightly different frequencies overlap. This overlap creates a "pulsating" effect—what you perceive as beats.

Imagine you have two waves: one with a frequency of 440 Hz (Hertz) and another with 444 Hz. The beat frequency is the difference between these two, which in this case is 4 Hz. This means you would hear four beats per second as the waves interfere with each other.

• Beat frequency = |f₁ - f₂|
• Occurs due to interference of close frequencies.
• Results in a pulsing sound pattern.

In the context of the police siren, the fluctuations in sound help create the distinct tonal shifts you hear as the siren changes its position relative to you. This is not just an interesting auditory phenomenon, but also plays a critical role in how we perceive sounds moving in our environment.

Wave Frequency

Wave frequency refers to the number of times a wave repeats itself within one second. The frequency of a wave is measured in Hertz (Hz), and it determines the "pitch" of the sound that we hear. Higher frequencies are perceived as higher pitches, while lower frequencies sound lower.

Wave frequency plays an especially crucial role when it comes to understanding the Doppler effect, which is what happens to sound waves when a police car moves towards or away from an observer.

• Frequency: Number of wave cycles per second.
• Measured in Hertz (Hz).
• Relates directly to the pitch we hear.
• Key to understanding Doppler effect shifts.

As a police car approaches you, the frequency of the siren you hear becomes higher due to the waves being compressed. Conversely, as the car drives away, the frequency decreases because the waves spread out. Thus, wave frequency not only tells us the pitch but also provides us insights into the movement of sound sources relative to us.

Sound Waves

Sound waves are vibrations that travel through the air, or any other medium, reaching your ears and allowing you to perceive sound. They are characterized by their frequency, wavelength, and amplitude.

When the police siren is in action, the Doppler effect alters the sound waves reaching a stationary observer, like a pedestrian. As these waves compress or expand due to the motion of the sound source (the police car), there is a noticeable change in frequency and pitch.

• Sound waves: Vibrations traveling through a medium.
• Characterized by frequency and wavelength.
• Interacts with phenomena like the Doppler effect.

Sound waves are fundamental in various fields, from music to communication. Understanding how they change in different scenarios, such as when affected by the Doppler effect in a moving siren, is essential for both scientific and practical reasons.