Oscillations and waves

Physical and perceptual characteristics of sound

Pitch relates to fundamental frequency, perceived loudness depends on sound level and hearing, and timbre reflects spectral structure and waveform.

The same musical note can sound different on a flute and a violin; even the same physical level is not perceived identically by everyone. Distinguish measurable quantities from auditory sensations.

L_I=10log_{10}!left( rac{I}{I_0} ight) mathrm{dB},qquad I_0=10^{-12} mathrm{W,m^{-2}}

Definition: Pitch, loudness, and timbre

Perceived pitch is mainly associated with fundamental frequency. Sound intensity level $L_I$ is a logarithmic physical quantity, not the same as loudness; loudness also depends on frequency, duration, and listener. Timbre depends on harmonics, spectrum, and time evolution.

Change frequency and harmonics to see pressure waveform change; pitch tracks the fundamental, while timbre reflects spectrum.

Sound level and spectrum

The level relative to reference intensity $I_0$ is measured in decibels; a 10 dB increase means ten times the intensity, but perceived loudness does not follow a single fixed ratio. A pure tone has one frequency; instruments usually produce complex tones with a fundamental and harmonics.

Example: Example

A sound has intensity $I=10^{-6}$ W/m². Find its level relative to $I_0=10^{-12}$ W/m².

Solution

$L_I=10log_{10}(10^6)=60$ dB. This is the intensity level; perceived loudness also depends on the listener.

Quick check

Two sounds with the same fundamental pitch and intensity level can differ in timbre because their harmonics have different relative amplitudes. A spectrum displays frequency components; the time envelope helps distinguish attack, sustain, and decay. Perception also depends on hearing and listening level, so a dB measurement alone cannot predict everyone’s sensation precisely.

When applying a model, state which quantities are held fixed and choose the appropriate reference frame. Keeping units beside numerical values helps prevent confusion between quantities or between measured and predicted values. After calculating, check dimensions, signs, and limiting cases: the result should fit the assumptions, such as small oscillations, a uniform medium, or negligible resistance. If real conditions differ, explain the discrepancy instead of applying a formula mechanically.

A useful physical check is to substitute special cases into the relation: equilibrium, maximum displacement, one full cycle, or no relative motion. These cases often make a quantity vanish or reach an extreme, exposing sign errors and confusion between period and frequency. When comparing experiments, change one condition at a time so that the cause of a changed result is clear.

A sound has $I=100I_0$ . What is its intensity level?

Which feature chiefly gives two instruments playing the same note different timbres?

References

Young, Freedman (2019). University Physics