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.
| Perception or quantity | Physical driver | Unit or measure | Common error |
|---|---|---|---|
| Pitch | frequency | Hz | saying amplitude controls pitch |
| Loudness | intensity/amplitude | W m^-2 or dB | treating dB as linear |
| Timbre | harmonic content | spectrum shape | saying only frequency matters |
| Resonance | frequency match | natural frequency | saying resonance is just "louder" |
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
-
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.
-
Pitch is mainly determined by:
- A. intensity
- B. frequency
- C. distance only
- D. air pressure only
Answer: B.
-
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.
-
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.
-
Use the point-source model:
$$I = \frac{P}{4\pi r^2}$$
-
Substitute:
$$I = \frac{2.4}{4\pi(3.0)^2}$$
-
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:
- identify the system,
- state that the driving frequency matches a natural frequency,
- relate the frequency match to large-amplitude standing waves,
- connect the claim to nodes/antinodes or pipe length if data are supplied.
Maintenance Loop
Short retrieval:
- Pitch corresponds mainly to ______.
- Loudness relates to ______.
- A 10-times intensity increase corresponds to ______ dB.
- Resonance occurs when a driving frequency matches a ______ frequency.