Problem 100 - Pearson Physics

Question

Triple Choice You stand near the tracks as a train approaches with constant speed. The train is blowing its horn continuously, and you listen carefully to the sound it makes. For each of the following properties of the sound, state whether it increases, decreases, or stays the same as the train gets closer: (a) intensity; (b) frequency; (c) wavelength; (d) wave speed.

Step-by-Step Solution

Answer

(a) Increases; (b) Increases; (c) Decreases; (d) Stays the same.

Step 1: Understanding Intensity

Intensity refers to the power per unit area carried by the wave. As the train approaches, the sound waves produced by the horn are compressed because they are emitted by a moving source. This leads to an increased amplitude or intensity of the sound waves reaching the observer. **Answer:** The intensity of the sound increases as the train gets closer.

Step 2: Analyzing Frequency

Frequency is the number of waves that pass a point per unit of time. Due to the Doppler effect, when the source of the sound, the train, is moving towards the observer, the sound waves are compressed, increasing their frequency. **Answer:** The frequency of the sound increases as the train gets closer.

Step 3: Considering Wavelength

Wavelength is the distance between successive crests of a wave. As the frequency increases due to the Doppler effect, the wavelength decreases because the waves are compressed. **Answer:** The wavelength of the sound decreases as the train gets closer.

Step 4: Evaluating Wave Speed

Wave speed refers to the speed at which the wave propagates through the medium. The speed of sound in air is constant and does not change whether the source is moving or stationary. **Answer:** The wave speed of the sound stays the same as the train gets closer.

Key Concepts

Sound Frequency

Sound frequency refers to the number of sound waves that pass a given point in one second, measured in hertz (Hz). When a sound source, like a train horn, moves towards you, the sound waves are compressed. This phenomenon is known as the Doppler Effect. As the waves get squeezed, their frequency increases.

This is why a train's horn sounds higher-pitched as it approaches you. The opposite happens when the train moves away; the frequency decreases and the pitch lowers.

• Compression of waves leads to higher frequency.
• When moving away, waves spread out, reducing frequency.

This change in frequency due to motion is a key way the Doppler Effect works.

Sound Intensity

Sound intensity is about how much power the sound wave carries per unit area. As a train with a blowing horn approaches you, the intensity of the sound increases. The reason is simple: the sound waves become denser, and more waves hit your ears per second.

The reason for this increase in intensity is not just about the Doppler Effect but also because you are getting closer to the sound source. As distance decreases, intensity naturally rises because the sound's power is more concentrated.

• Measured in decibels (dB).
• Increases as distance to the source decreases.

This effect makes sounds appear louder the closer you are to the origin of the sound.

Sound Wavelength

Wavelength is the distance between consecutive peaks of a wave. It’s directly related to the speed and frequency of the wave by the equation \[ \text{Wavelength} = \frac{\text{Wave Speed}}{\text{Frequency}} \].

As a train moves closer, the sound wavelength decreases due to increased frequency (because of the Doppler Effect). The waves are literally getting compressed as they travel from a moving source towards you.

• Shorter wavelength = higher frequency when source approaches.
• Longer wavelength = lower frequency when source moves away.

Understanding wavelength changes helps in visualizing how the pitch and sound experience shifts with movement.

Wave Speed

Wave speed is the rate at which a wave travels through a medium. For sound, this is typically through air. Importantly, wave speed doesn’t change even if the train is moving. In calm air conditions, sound travels at a speed of approximately 343 meters per second.

Whether the sound source is stationary or moving, this speed remains constant because it is determined by properties of the air like temperature, humidity, and pressure, not by the motion of the source.

• Depends on the medium, not the source motion.
• Constant under stable weather conditions.

This constancy means while frequency and wavelength may change due to motion, wave speed remains unaffected by the Doppler Effect.