Problem 19 - An Introduction to Physical Science

Question

How is the wavelength of sound affected when (a) a sound source moves toward a stationary observer, and (b) the observer moves away from a stationary sound source?

Step-by-Step Solution

Answer

(a) The wavelength decreases; (b) the wavelength increases.

Step 1: Understand the Doppler Effect

The change in wavelength of sound is explained by the Doppler Effect. This effect describes how the frequency (and thus, wavelength) of a wave changes in relation to an observer when the source or the observer is moving.

Step 2: Determine Effect in Case (a)

When the sound source moves toward a stationary observer, the sound waves in front of the source are compressed. This leads to a decrease in wavelength and an increase in frequency. Hence, the wavelength decreases.

Step 3: Determine Effect in Case (b)

When the observer moves away from a stationary sound source, the waves seem to stretch out from the perspective of the observer. This increases the wavelength and decreases the perceived frequency. Hence, the wavelength increases.

Key Concepts

Wavelength of Sound

Wavelength in sound refers to the physical distance between corresponding points of consecutive cycles (such as peaks) of a sound wave. The wavelength has an inverse relationship with frequency, which means when the frequency is high, the wavelength is short and vice versa.

As sound travels through a medium like air, its speed is constant. When a sound source moves, it affects the wavelength due to compressing or stretching of the sound waves. Understanding how wavelength is altered by motion is crucial for comprehending the Doppler Effect.

Frequency Change

When discussing sound waves, frequency refers to how many sound wave cycles pass a given point per second, measured in Hertz (Hz). It is essential because it's directly related to what we hear as pitch.

As the source or observer of a sound moves, this frequency can change due to the Doppler Effect. If the frequency increases, you hear a higher pitch, while a decrease results in a lower pitch.

• When the source moves toward an observer, the frequency rises.
• Conversely, if the source moves away, the frequency falls.

These changes in frequency directly affect the perceived sound, making the Doppler Effect a fascinating phenomenon.

Moving Sound Source

A moving sound source changes how sound waves reach an observer, significantly affecting both wavelength and frequency.

When the source moves toward an observer, sound waves are compressed, leading to shorter wavelengths and higher frequencies. This compression is why sirens from an approaching emergency vehicle sound higher in pitch.

If the source moves away, the opposite occurs. Waves stretch out, increasing the wavelength and lowering the frequency, which results in a drop in the perceived pitch as the vehicle moves away.

Stationary Observer

In scenarios with a stationary observer, the changes in perceived sound depend solely on the movement of the sound source. The observer is not moving within the sound field, but how they perceive the sound can change dramatically.

If a sound source approaches them, the sound waves compress, resulting in a higher frequency and lower wavelength as they reach the observer. This is why trains sound different as they come closer.

On the other hand, if the sound source moves away, the observer perceives stretched-out waves, leading to a lower frequency and thus a lower pitch.

Observer Movement

When the observer is in motion, their movement affects how they perceive the sound's wavelength and frequency.

If the observer moves towards the stationary sound source, they encounter sound waves more frequently, resulting in a decreased wavelength and increased frequency. The sound seems to increase in pitch.

Conversely, if the observer moves away, they perceive the sound waves less frequently. This perception increases the wavelength and decreases the frequency, causing the sound to lower in pitch. This phenomenon is crucial in understanding how movement influences sound perception in everyday life.