Lecture 21: Musical Sounds Study Guide

Conceptual Distinction: The difference between music and noise is the combination of different frequencies and amplitudes of sound.
- Musical Sounds: Generally categorized as combinations of frequencies that are pleasing to the listener. Examples include genres such as jazz, classical, rock, or rap.
- Noise: Categorized as sounds that are not pleasing to the listener. Examples include banging together pots and pans or dropping a hammer on the floor.
Subjectivity: To a certain extent, distinguishing music from noise is a subjective process. One individual may consider a sound to be musical while another considers it noise.
Physics Perspective: Scientists broadly categorize sounds based on the specific types of frequencies they contain.
- Most sounds are not "pure tones" (consisting of only a single frequency) but are combinations of few or many different tones.

Definition of Fourier Analysis: A method used to examine the different individual frequencies that make up a specific sound wave. The mathematical complexity of Fourier analysis is significant and often requires specialized software.
Software Application: Software such as Logger Pro can record a sound wave and generate a Fourier analysis graph of amplitude versus frequency. This allows researchers to see:
- Which frequencies are represented in a specific sound wave.
- The relative loudness (amplitude) of each frequency component.
Types of Fourier Analysis Distributions:
- Discrete: Characteristic of musical sounds (e.g., tuning forks, pianos) where only a few specific frequencies exist.
- Continuous/Random: Characteristic of noise (e.g., finger snaps, white noise) where frequency distributions are broad or lack a clear pattern.

Tuning Fork:
- Designed to produce a single frequency.
- Analysis shows a single predominant peak at $490\,Hz$ (the frequency stamped on the side of the fork).
- Other harmonics may exist but are present at greatly reduced amplitudes.
Piano:
- When playing a single note, it does not produce a single frequency wave.
- It contains more frequencies than a tuning fork.
- The frequencies are periodic, meaning they are spaced out at regular intervals.
Finger Snap:
- Produces many different frequencies of sound waves.
- The Fourier analysis graph appears random with no clear pattern to the frequencies.
White Noise Machine:
- Creates a very broad spectrum of frequencies represented in the sound wave.

Harmonics and Standing Waves: Musical instruments are designed to support different standing waves, creating sounds at various frequencies.
The Problem of Middle C: If five different instruments play "middle C" at a frequency of approximately $260\,Hz$ , they still sound distinct from one another.
Definition of Timbre: The characteristic that causes different instruments to sound different even when playing the same note at the same fundamental frequency.
- Timbre is determined by the specific Fourier analysis of the instrument.
- It depends on the design of the instrument, the materials used in its construction, and the specific composition of harmonics created.

Loudness: A subjective quality related to the amplitude of a sound wave. It cannot be universally agreed upon, as one person may find a volume level pleasing while another finds it too loud.
Intensity: An objective, physical quantity that can be measured. It describes the energy per unit of area reaching a specific location every second.
- Formula: Intensity is equal to the amount of power ( $P$ ) divided by the area ( $A$ ) over which that power is distributed.
- Units: The units of intensity are watts per meter squared ( $W/m^2$ ).

The human ear can detect an enormous range of intensity values:
- Threshold of Human Hearing (Quiet): $10^{-12}\,W/m^2$ (represented as $0.000000000001\,W/m^2$ ).
- Rocket Engine (Loud): $10^{6}\,W/m^2$ (represented as a one followed by six zeros).
Relative Intensity Scale: Because the range of absolute intensity is so vast, scientists use a relative scale based on the threshold of human hearing ( $10^{-12}\,W/m^2$ ).
- The relative intensity of the threshold of hearing is 1.
- The relative intensity of a rocket engine is $10^{18}$ .

Logarithmic Scale: To manage the large range of values, scientists use a logarithm (which looks at the exponent of the power of ten while ignoring the base).
- Threshold of human hearing on a log scale: 0.
- Rocket engine on a log scale: 18.
The Decibel (dB) Scale: The final scale used to discuss sound intensity. It is calculated by taking the logarithm of the relative intensity and multiplying by 10.
Safety Thresholds:
- Hearing Damage: Exposure to sounds around $85\,dB$ can cause permanent damage to the ears over time.
- Physical Pain: Sound waves cause physical pain at approximately $120\,dB$ .

Methods of Protection:
- Earplugs: Sufficient for short exposures or relatively low intensity noises.
- Earmuffs: Necessary for longer exposures or more intense noises, such as working near jet engines.
Calculating Intensity Reduction: Earplug packages include a decibel value indicating the reduction in intensity.
- Example: A gas-powered leaf blower at $90\,dB$ paired with $30\,dB$ earplugs reduces the perceived intensity to $60\,dB$ .

Because the decibel scale is logarithmic, comparing intensities involves powers of ten.
Increasing the decibel value by 10 results in multiplying the physical intensity by 10.
- 10 dB difference: 10 times more intense.
- 20 dB difference: 100 times more intense ( $10 \times 10$ ).
- 30 dB difference: 1000 times more intense ( $10 \times 10 \times 10$ ).
Jet Engine vs. Rocket Engine Example:
- Jet engine: $150\,dB$ .
- $160\,dB$ is 10 times more intense than a jet engine.
- $170\,dB$ is 100 times more intense than a jet engine.
- Rocket engine ( $180\,dB$ ) is 1000 times more intense than a jet engine.