Characteristics of Sound Waves

Sound is a longitudinal mechanical wave produced by vibrating objects. In the study of sound, we distinguish between musical notes and noise, and explore the physical properties that define how we perceive sound.

1. Noise and Musical Notes

Musical Note: This is a sound produced by a source vibrating at regular, periodic intervals. It has a definite frequency and is pleasing to the ear.

Noise: This is a sound produced by a source vibrating at irregular, non-periodic intervals. It lacks a definite frequency and is often perceived as unpleasant.

2. Characteristics of Sound

• Pitch: This depends on the frequency of the sound wave. High-frequency waves produce high-pitched sounds, while low-frequency waves produce low-pitched sounds.
• Loudness and Intensity: Loudness is a subjective sensation of the ear, while intensity is the energy transmitted per unit time across a unit area. Both depend on the amplitude of the sound wave. Loudness also depends on the sensitivity of the ear.
• Quality (Timbre): This is the property that allows us to distinguish between two notes of the same pitch and loudness produced by different musical instruments. It depends on the number and relative intensity of the overtones (harmonics) present.

3. Vibrating Strings

The fundamental frequency (f₀) of a vibrating string is given by the formula:

f₀ = (1 / 2L) * √(T / μ)

Where:

• L = length of the string
• T = tension in the string
• μ = mass per unit length (m/l)

4. Resonance

Resonance occurs when a system is made to vibrate at its natural frequency by another vibrating system. Acoustic examples include:

• A tuning fork held over a resonating air column.
• Vibrations of a guitar body amplifying the sound of the strings.
• Shattering a glass with a high-pitched voice.

5. Air Columns (Pipes)

Closed Pipes: These are closed at one end. They produce only odd harmonics. The fundamental frequency is f₀ = v / 4L. The ratio of frequencies is 1:3:5.

Open Pipes: These are open at both ends. They produce both even and odd harmonics. The fundamental frequency is f₀ = v / 2L. The ratio of frequencies is 1:2:3.