Describe how changes in amplitude and frequency affect the loudness and pitch of sound waves

3.4 Sound

Objective

Describe how changes in amplitude and frequency affect the loudness and pitch of sound waves.

Key Concepts

• Amplitude – the maximum displacement of particles in the medium from their rest position.
• Frequency (f) – the number of complete vibrations (cycles) that occur each second, measured in hertz (Hz).
• Loudness – the perceived strength of a sound, related to the intensity of the wave.
• Pitch – the perceived highness or lowness of a sound, directly related to its frequency.

Amplitude and Loudness

The intensity (I) of a sound wave is proportional to the square of its amplitude (A):

\$I \propto A^{2}\$

Loudness is a logarithmic response to intensity. The sound level (L) in decibels (dB) is given by:

\$L = 10 \log{10}\!\left(\frac{I}{I{0}}\right)\$

where \(I_{0}\) is the reference intensity (the threshold of hearing, \(1 \times 10^{-12}\,\text{W m}^{-2}\)).

• Increasing amplitude → larger intensity → higher sound level → louder sound.
• Decreasing amplitude → lower intensity → lower sound level → softer sound.

Frequency and Pitch

Pitch is directly related to the frequency of the sound wave:

\$\text{Pitch} \propto f\$

• Higher frequency (more cycles per second) → higher pitch (e.g., a whistle).
• Lower frequency (fewer cycles per second) → lower pitch (e.g., a drum).

Human hearing typically ranges from about 20 Hz to 20 kHz. Within this range, the ear can distinguish small changes in frequency as changes in pitch.

Combined Effects

Amplitude and frequency affect different perceptual qualities, but both can change simultaneously in real sounds. For example, a musical instrument may produce a louder note (greater amplitude) that is also higher in pitch (greater frequency).

Summary Table

Practical Examples

1. String instrument (e.g., guitar) – Plucking a string tighter (higher tension) increases frequency, giving a higher pitch. Striking the string harder increases amplitude, making the note louder.
2. Loudspeaker – Turning up the volume control raises the amplitude of the electrical signal, producing a louder sound without changing the pitch.
3. Human voice – Speaking loudly involves greater air pressure variations (higher amplitude). Changing the shape of the vocal cords changes frequency, altering pitch.

Common Misconceptions

• “Loudness is the same as pitch.” – Loudness depends on amplitude/intensity, while pitch depends on frequency.
• “A higher pitch always sounds louder.” – Pitch and loudness are independent; a high‑frequency tone can be very soft if its amplitude is low.

Key Take‑away

In sound waves, amplitude determines loudness (through intensity and the decibel scale), while frequency determines pitch**. Understanding these relationships helps explain everyday phenomena and is essential for analysing musical sounds, acoustic engineering, and health‑related topics such as hearing loss.