Problem 100 - Pearson Physics

Question

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

Intensity increases, frequency increases, wavelength decreases, wave speed stays the same.

Step 1: Analyzing Intensity

Intensity of sound is related to its loudness as perceived by our ears, and it is a measure of the power per unit area. As the train gets closer, the intensity increases because the distance to the sound source decreases, leading to a higher sound level.

Step 2: Analyzing Frequency

The frequency of the sound refers to how many wave crests pass a point in one second, measured in Hertz (Hz). Due to the Doppler Effect, as the train approaches, the frequency increases because the train is moving towards the observer, compressing the sound waves.

Step 3: Analyzing Wavelength

The wavelength of sound is the distance between consecutive crests of the sound wave. As the train approaches, the wavelength shortens, or decreases, because the waves are compressed in front of the moving train.

Step 4: Analyzing Wave Speed

The speed of sound in air is generally constant under constant conditions of temperature and pressure. Thus, the wave speed stays the same, regardless of the train's movement.

Key Concepts

sound intensity

Sound intensity refers to how loud a sound appears to our ears. It is defined as the amount of sound energy passing through a unit area every second. Essentially, it's a measure of how much sound power is hitting us. When a sound source, like a train horn, gets closer to you, the intensity of the sound increases. This happens because the sound waves have less distance to travel, concentrating more energy into a smaller area. As the train approaches, the sound becomes louder, a clear indicator that the sound intensity is rising.

• The closer the source, the greater the intensity.
• Measured in decibels (dB).

Generally, increased sound intensity isn't just about how loud the sound is but also affects the energy delivered to your ears.

sound frequency

Sound frequency relates to how often the sound waves pass a certain point each second, measured in Hertz (Hz). Think of it as the pitch of the sound. In the context of the train beyond the textbook problem, we introduce the Doppler Effect here to explain frequency changes. The Doppler Effect occurs when a sound source moves relative to an observer. As the train approaches, the sound waves get bunched up, leading to a higher frequency or pitch. As a result, you hear a higher-pitched sound as the train gets closer, indicative of an increase in frequency.

• High frequency = higher pitch.
• Frequency increases as distance decreases.

Once the train passes by and starts moving away, the frequency will lower, and you will hear a lower pitch.

wavelength

The wavelength of a sound is the distance from one wave crest to the next. It can be thought of as the physical length of one complete wave cycle. In our train scenario, as the train gets closer, the distance between the crests of the sound waves decreases. This results in shorter wavelengths due to the compression of waves in front of the moving train. Thus, the wavelength decreases as the train approaches.

• Wavelength is inversely related to frequency.
• Shorter wavelengths are produced by higher frequency sounds.

Understanding wavelength changes helps explain the Doppler Effect in terms of wave behavior.

wave speed

Wave speed is how fast the sound wave moves through the medium, usually air. In this context, it's crucial to know that the speed of sound in air remains fairly constant at around 343 meters per second (under standard conditions of temperature and pressure). Interestingly, the train's movement towards or away from you doesn't alter the actual speed of sound itself. While the perception of frequency and wavelength might change due to the Doppler Effect, the wave speed remains unchanged.

• Relatively constant under given conditions.
• Unaffected by the Doppler Effect.

This concept highlights that wave speed is independent of the source's motion, making sound wave speed reliable, regardless of movement.