Detection of sound, pitch, and loudness

1. Detection of Sound

How Sound Is Produced

  • Sound is created by vibrations.

  • Vibrations create alternating regions of:

    • Compression (high pressure)

    • Rarefaction (low pressure)

  • These pressure changes travel through a medium as sound waves.

Example: Acoustic Guitar

  1. String vibrates.

  2. Guitar body vibrates.

  3. Air moves in and out of sound hole.

  4. Compressions and rarefactions form.

  5. Sound wave travels through air.

2. Sound Intensity and Distance

Sound Intensity

  • Intensity measures how much sound energy passes through an area.

  • Sound becomes weaker as distance from the source increases.

Inverse Square Law

I∝1r2I \propto \frac{1}{r^2}I∝r21​

Where:

  • III = intensity

  • rrr = distance from source

Important Relationship

If distance doubles:

I∝1(2r)2I \propto \frac{1}{(2r)^2}I∝(2r)21​I∝14r2I \propto \frac{1}{4r^2}I∝4r21​

Result:

  • Double distance → intensity becomes 1/4

  • Triple distance → intensity becomes 1/9

  • Four times distance → intensity becomes 1/16

Exam Fact: Sound gets quieter very quickly as distance increases.

3. Sound Interference

Interference

Occurs when two sound waves meet in the same medium.

Constructive Interference

  • Compression meets compression.

  • Rarefaction meets rarefaction.

  • Amplitudes add together.

Result:

  • Louder sound

Destructive Interference

  • Compression meets rarefaction.

Result:

  • Smaller amplitude

  • Quieter sound

Complete Destructive Interference

If both waves have equal amplitude:

A+(−A)=0A + (-A) = 0A+(−A)=0

Result:

  • No sound heard

4. The Human Ear

The ear converts:

Sound Energy → Electrical Signals → Brain Interpretation

Main Parts of the Ear

Outer Ear

Contains:

  • Pinna

  • Ear canal

  • Eardrum

Function:

  • Collects sound waves.

  • Directs them toward eardrum.

Middle Ear

Contains three tiny bones:

  1. Hammer (Malleus)

  2. Anvil (Incus)

  3. Stirrup (Stapes)

Function:

  • Amplify vibrations.

  • Transfer vibrations to oval window.

Inner Ear

Contains:

  • Cochlea

  • Semicircular canals

Function:

  • Converts vibrations into nerve impulses.

Sound Detection Process

  1. Sound enters pinna.

  2. Travels through ear canal.

  3. Eardrum vibrates.

  4. Hammer, anvil, and stirrup vibrate.

  5. Oval window vibrates.

  6. Fluid inside cochlea moves.

  7. Hair cells detect movement.

  8. Hair cells create electrical signals.

  9. Signals travel to brain.

  10. Brain interprets sound.

5. Pitch

Definition

Pitch is the perception of frequency.

Relationship

Higher Frequency→Higher Pitch\text{Higher Frequency} \rightarrow \text{Higher Pitch}Higher Frequency→Higher PitchLower Frequency→Lower Pitch\text{Lower Frequency} \rightarrow \text{Lower Pitch}Lower Frequency→Lower Pitch

Examples

  • Violin = high pitch

  • Bass guitar = low pitch

Human Hearing Range

20 Hz  to  20,000 Hz20 \text{ Hz} \; \text{to} \; 20,000 \text{ Hz}20 Hzto20,000 Hz

Frequency Categories

Frequency

Perception

Low frequency

Low pitch

High frequency

High pitch

Cochlea Function

  • Low frequencies detected near center.

  • High frequencies detected near entrance.

6. Loudness

Definition

Loudness is the perception of amplitude.

Relationship

Higher Amplitude→Louder Sound\text{Higher Amplitude} \rightarrow \text{Louder Sound}Higher Amplitude→Louder SoundLower Amplitude→Softer Sound\text{Lower Amplitude} \rightarrow \text{Softer Sound}Lower Amplitude→Softer Sound

Example

Plucking a guitar harder:

  • Greater amplitude

  • Greater pressure differences

  • Louder sound

7. Sound Intensity

Definition

Sound intensity = energy transported per second through a unit area.

Unit

W/m2W/m^2W/m2

(Watts per square meter)

Threshold of Hearing

Smallest intensity humans can hear:

1×10−12  W/m21 \times 10^{-12} \; W/m^21×10−12W/m2

Called:
Threshold of Hearing

8. Decibel Scale

Because the ear detects an enormous range of intensities, a logarithmic scale is used.

Unit

  • Bel (B)

  • Decibel (dB)

1  B=10  dB1 \; B = 10 \; dB1B=10dB

Reference Levels

Sound Level

Intensity

0 dB

1×10−121 \times 10^{-12}1×10−12 W/m²

10 dB

1×10−111 \times 10^{-11}1×10−11 W/m²

20 dB

1×10−101 \times 10^{-10}1×10−10 W/m²

Each increase of:

  • 10 dB = 10× greater intensity

Common Sound Levels

Sound Source

Approx. dB

Threshold of hearing

0 dB

Rustling leaves

10 dB

Normal conversation

60 dB

Acoustic guitar (1 ft away)

80 dB

Subway train

100 dB

Pain threshold

130 dB

Eardrum rupture

160 dB

Hearing Damage

Safe Range

  • Below 80 dB generally safe

Dangerous Range

  • Above 80 dB for long periods can damage cochlear hair cells.

Examples:

  • Lawnmowers

  • Loud concerts

  • Headphones at high volume

Severe Damage

130 dB:

  • Pain begins

160 dB:

  • Possible eardrum rupture

  • Immediate hearing loss

Key Facts to Memorize

  • Sound intensity follows the inverse square law:

I∝1r2I \propto \frac{1}{r^2}I∝r21​

  • Double distance → intensity becomes 1/4.

  • Constructive interference → louder sound.

  • Destructive interference → quieter sound.

  • Pitch depends on frequency.

  • Loudness depends on amplitude.

  • Human hearing range: 20 Hz – 20,000 Hz.

  • Threshold of hearing:

1×10−12W/m21 \times 10^{-12} W/m^21×10−12W/m2

  • Sound intensity measured in W/m².

  • Sound level measured in decibels (dB).

  • 130 dB causes pain.

  • 160 dB can rupture the eardrum.

  • Hair cells in the cochlea convert vibrations into electrical signals for the brain.