Sound Waves

Orientation

Lesson goal: connect sound-wave properties to pitch, loudness, intensity, resonance, and standing-wave behaviour.

The main writing discipline is to keep physical quantities separate from human perception. Pitch is not loudness, and intensity is not frequency.

Core Content

Sound in air is a longitudinal pressure wave. Air particles oscillate parallel to the direction of energy transfer, producing compressions and rarefactions.

Key equations:

$$v = f\lambda$$

$$I = \frac{P}{A}$$

$$\beta = 10\log_{10}\left(\frac{I}{I_0}\right)$$

For a point source spreading sound uniformly:

$$I = \frac{P}{4\pi r^2}$$

Concept Check

1. Sound in air is mainly:

   • A. transverse displacement of air upward and downward
   • B. longitudinal pressure variation
   • C. electromagnetic radiation
   • D. static charge transfer

   Answer: B.

2. Pitch is mainly determined by:

   • A. intensity
   • B. frequency
   • C. distance only
   • D. air pressure only

   Answer: B.

3. Increasing sound intensity by a factor of 10 changes sound level by:

   • A. 1 dB
   • B. 3 dB
   • C. 10 dB
   • D. 100 dB

   Answer: C.

4. Short response: explain why increasing amplitude does not necessarily change pitch.

Applied Practice

Worked Example

A speaker emits sound power $2.4\ \text{W}$ uniformly. Find the intensity $3.0\ \text{m}$ from the source.

1. Use the point-source model:

   $$I = \frac{P}{4\pi r^2}$$

2. Substitute:

   $$I = \frac{2.4}{4\pi(3.0)^2}$$

3. Calculate:

   $$I = 2.12 \times 10^{-2}\ \text{W m}^{-2}$$

Final answer: $I = 2.1\times10^{-2}\ \text{W m}^{-2}$. The answer assumes uniform spreading and ignores room reflections.

Practice Problem

A source emits $1.0\ \text{W}$ of sound power uniformly. Calculate the intensity at $2.0\ \text{m}$ and state one limitation of the model in a classroom.

Deep Practice And Writing

Prompt: explain resonance in an air column. Your answer must identify the driving frequency, natural frequency, and standing-wave pattern.

Strong response pattern:

1. identify the system,
2. state that the driving frequency matches a natural frequency,
3. relate the frequency match to large-amplitude standing waves,
4. connect the claim to nodes/antinodes or pipe length if data are supplied.

Tutor Context

Use this lesson context when the student asks about:

• pitch versus loudness,
• sound as a longitudinal wave,
• intensity and inverse-square spreading,
• decibel scale,
• resonance and standing waves in air columns.

Tutor should first check whether the student is mixing amplitude, intensity, frequency, and pitch.

Useful tutor diagnostic:

If a sound becomes louder but the source frequency does not change, what perceptual feature changes and what feature should stay the same?

Maintenance Loop

Short retrieval:

1. Pitch corresponds mainly to ______.
2. Loudness relates to ______.
3. A 10-times intensity increase corresponds to ______ dB.
4. Resonance occurs when a driving frequency matches a ______ frequency.

Source Trace

This lesson is materialised from the existing textbook section, app lesson YAML, roadmap lesson, roadmap concept questions, and Module 3 notes. It is ready for conversion into a typed content manifest and panelled-course render block.