2.3 Amplitude and sound intensity

Sound waves have two key properties: amplitude and intensity. Amplitude measures the wave's height, while intensity quantifies its energy. These concepts are crucial for understanding how we perceive and measure sound in our daily lives.

Decibels provide a practical way to express sound levels, using a logarithmic scale that matches human hearing. This system allows us to compare vastly different sound intensities, from a whisper to a jet engine, using a single, intuitive scale.

Amplitude and Sound Intensity

Amplitude and sound intensity

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• Amplitude measures maximum displacement of a wave from equilibrium position in units of distance (meters)
• Sound intensity quantifies rate of energy transfer through unit area measured in watts per square meter (W/m²)
• Intensity proportional to square of amplitude ($I \propto A^2$) doubling amplitude quadruples intensity
• Amplitude visualized as height of sound wave peaks and troughs (ocean waves)
• Intensity analogous to power of sound wave striking surface (sunlight intensity on Earth)

Decibel calculations

• Sound Intensity Level (SIL) formula: $SIL = 10 \log_{10}(\frac{I}{I_0})$ dB where $I_0 = 10^{-12}$ W/m² (reference intensity)
• Sound Pressure Level (SPL) formula: $SPL = 20 \log_{10}(\frac{P}{P_0})$ dB where $P_0 = 2 \times 10^{-5}$ Pa (reference pressure)
• Intensity and pressure relationship: $I = \frac{P^2}{\rho c}$ ($\rho$ air density, $c$ speed of sound)
• SIL calculation example: 100 times reference intensity yields 20 dB
• SPL calculation example: 10 times reference pressure yields 20 dB

Logarithmic nature of decibels

• Compresses wide range of values into manageable numbers facilitating easy comparison of vastly different intensities
• Human ears respond logarithmically to sound intensity changes perceived loudness doubles with every 10 dB increase
• Matches human auditory perception simplifies calculations involving large intensity ratios
• Dynamic range of human hearing spans approximately 120 dB from threshold of hearing to threshold of pain
• Logarithmic scale example: 80 dB perceived as twice as loud as 70 dB not eight times louder

Typical sound intensity levels

• Quiet environments: whisper (20-30 dB) library (30-40 dB) quiet suburban area (40-50 dB)
• Moderate noise levels: normal conversation (60-70 dB) busy office (70-80 dB) city traffic inside car (80-85 dB)
• Loud environments: lawn mower (90-95 dB) rock concert (100-120 dB) jet engine at takeoff (130-140 dB)
• Threshold values: hearing (0 dB) pain (120-140 dB)
• Everyday examples: refrigerator hum (40 dB) washing machine (70 dB) motorcycle (95 dB)