Lecture 2 Notes

General Reminders

• Labs next week; reading is beneficial but not assessed.

• Read in advance for the following week's assessed lab.

• Auditory filter section coming up, aligning with the lab in two weeks; aiming to start by the end of this lecture or on Friday.

Specifying Sound Amplitude

• Amplitude: Height of a sine wave; corresponds to loudness.

• Higher amplitude generally leads to greater loudness; complexities to be explored later.

Quantifying Physical Properties of Sound

• Goal: To quantify sound amplitude for analysis and manipulation.

• Range of sound amplitudes is immense, making large numbers impractical.

• Solution: Use logarithms to compress the scale.

Decibel Scale

• Using logs to compress sound amplitudes leads to the decibel scale.

Decibel Equation

• $dB = 20 \times log<em>{10}(P/P</em>0)$

  • $log_{10}$: Base 10 logarithm.

  • P: Sound pressure level of the stimulus.

  • $P_0$: Sound pressure reference level (fixed value).

  • dB: Decibels.

Understanding Logarithms

• $log_{10}(1) = 0$

• $log_{10}(10) = 1$

• $log_{10}(100) = 2$

• $log_{10}(10000) = 4$

• Logarithms compress large number ranges into smaller ones.

Sound Pressure Level

• Reference level ($P_0$): 20 microPascals ($20 \mu Pa$ ).

• If $P_0$ = 20 $mu Pa$, dB becomes dB SPL (decibels sound pressure level).

Other Reference Levels

• Average threshold for a healthy young adult can be used as a reference.

• Results in dB HL (decibels hearing level), used clinically to assess hearing loss relative to the average.

Origin of 20 MicroPascals Reference

• Chosen because it's near the absolute threshold for a 1,000 Hz tone.

• Auditory system is most sensitive to tones around 1,000 Hz.

• Absolute threshold: Minimum level of a stimulus detectable by a person.

Pressure Ratio and dB SPL

• Pressure ratio: P / $P_0$

• When pressure ratio is 1, dB SPL is 0 (0 dB SPL is not silence, but the absolute threshold).

• Negative dB SPL means the sound is below the absolute threshold.

• Example: Pressure ratio of 10,000,000 corresponds to 140 dB SPL.

Usefulness of Decibel Scale

• Compresses a large range of sound amplitudes into a small range of dB SPL.

• Every 10 dB increase approximately doubles the perceived loudness.

• Tied to absolute thresholds and loudness perception.

Sound Complexity

• Complexity: Two or more simultaneous tones adding together.

• Single sine waves are rare in real-world sounds.

• Voice is complex.

Simplest Way to Approach Complexity

• Adding sine waves and musical instruments: Adding together a couple of sine waves to see what happens then starting to talk about complexity in terms of musical instruments.

Adding Sine Waves

• Sine waves add together at each point in time.

• Amplitudes at each point add together.

• Playing two sine waves results in a complex pattern of molecule movement.

Example

• Combining a 1,000 Hz and a 2,000 Hz tone.

• Complex sounds comprise from dozens to thousands of components.

Describing Complex Sounds

• Challenge: Need a simpler way to describe complex sounds with multiple components.

• Limiting to harmonic stimuli (e.g., musical instruments).

Fundamental Frequency

• Fundamental frequency: Lowest frequency in a complex sound.

• Harmonic is also the fundamental frequency.

• Harmonics are integer multiples of the fundamental frequency.

Examples of Harmonics

• If 1,000 Hz is the fundamental frequency.

• 2,000 Hz is a harmonic (1,000 x 2).

• 3,000 Hz is another harmonic (1,000 x 3).

• 4,000 Hz is another harmonic (1,000 x 4).

• Harmonic sounds are made up only of harmonics (multiples of the fundamental frequency).

Visualizing Complex Sounds: Spectrum

• Represent frequency on the x-axis and amplitude on the y-axis.

• Each frequency component is represented by a vertical line.

• Spectrum helps compress complex visual representations into a simple format without losing information

Spectrum Analysis

• Spectrum: Frequency on the x-axis, amplitude on the y-axis.

• Fourier Transform: Converts time domain representation (amplitude vs. time) to frequency domain representation (amplitude vs. frequency).

• Inverse Fourier Transform: Converts frequency domain back to time domain (used in early sound sampling instruments).

• Fourier transform can decompose speech into it's constituent sine waves.

Physical Stimulus Limits of Sound Perception

• Sound levels and their potential dangers.

• 0 dB SPL: Absolute threshold.

• Sounds below 90 dB SPL: Generally safe for prolonged exposure.

• Sounds between 90-130 dB SPL: Cause hearing loss after prolonged exposure.

• Sounds above 130 dB SPL: Cause instant hearing loss.

Dangers of Headphones

• Turning up the volume to overcome background noise can easily exceed safe sound levels.

• Prolonged exposure leads to hearing loss (personal listening device (PLD)-induced hearing loss).

Frequency Ranges

• Mice: Up to 80,000 Hz.

• Dogs: Up to 50,000 Hz.

• Moths: Up to 130,000 Hz.

• Bats: Up to 120,000 Hz.

• Cats: Similar to dogs.

• Elephants: Up to 10,000 Hz.

• Humans: Up to 20,000 Hz (decreasing with age and ear damage).

Lowest Frequencies

• Humans: Down to about 20 Hz (felt more than heard).

• Elephants: Slightly lower than humans.

• Dogs: Down to 13 Hz.

• Cats: Not as low as dogs.

Kahoot Reminder

• Ensure you have Kahoot ready on your phone for the next session on Friday.