Unit
- Sound wave basics: Sound is a mechanical wave that propagates through a medium as variations in pressure. Frequency, measured in hertz (Hz), determines pitch, while amplitude relates to loudness. The human hearing range spans roughly 20 Hz to 20 kHz, and sound travels at approximately 343 meters per second in air at room temperature.
- Waveform characteristics: Simple waveforms include sine, square, triangle, and sawtooth. Each has a distinct harmonic content: sine waves contain only the fundamental, while square waves have odd-numbered harmonics. These shapes form the building blocks for synthesis and sound design.
- Phase and interference: Phase describes the position of a waveform in its cycle at a given time. Constructive interference occurs when waves align, increasing amplitude; destructive interference cancels sound. Phase cancellation is a common issue in recording and mixing, often addressed by careful microphone placement or polarity inversion.
- Harmonics and overtones: Most natural sounds consist of a fundamental frequency plus a series of harmonics (integer multiples of the fundamental). The relative strength of these harmonics determines timbre, the characteristic that distinguishes different instruments playing the same note.
- Acoustic envelope: The ADSR model (Attack, Decay, Sustain, Release) describes how a sound evolves over time. Attack is the time to reach peak amplitude, decay is the drop to sustain level, sustain holds until the note ends, and release is the fade-out. This model is central to synthesizer programming.
- Sound pressure level (SPL): Measured in decibels (dB), SPL quantifies the intensity of sound relative to a reference. The threshold of hearing is 0 dB SPL, while prolonged exposure above 85 dB can cause hearing damage. Understanding SPL is important for safe monitoring levels.
- Doppler effect: The perceived pitch of a sound source changes when either the source or listener moves. As a source approaches, frequency increases; as it recedes, frequency decreases. This effect is used creatively in sound design for movement and depth.
- Resonance and standing waves: Resonance occurs when an object vibrates at its natural frequency, amplifying that frequency. Standing waves form in enclosed spaces, creating peaks and nulls at specific frequencies. Room acoustics can be treated with absorbers and diffusers to minimize unwanted resonances.
- Inverse square law: In a free field, sound intensity decreases proportionally to the square of the distance from the source. Doubling the distance reduces intensity by 6 dB. This principle is essential for microphone placement, speaker positioning, and understanding natural sound decay. It explains why close miking captures more direct sound and less room ambience.
- Psychoacoustic masking: Psychoacoustic masking occurs when a louder sound makes a softer sound at a similar frequency inaudible. This frequency dependent effect is exploited in lossy audio compression algorithms like MP3, which discard masked information to reduce file size. Sound designers use masking principles to avoid conflicts between instruments, ensuring clarity in dense mixes.
- Fourier analysis: Fourier analysis states that any complex waveform can be represented as a sum of sine waves at different frequencies, amplitudes, and phases. The Fast Fourier Transform (FFT) enables real time spectrum analysis in digital audio workstations. Sound designers use FFT displays to identify problematic frequencies, verify harmonic structures, and apply targeted equalization. This mathematical foundation underpins modern audio processing techniques.
Code Example
Python
import numpy as np
import matplotlib.pyplot as plt
sample_rate = 44100
duration = 1.0
t = np.linspace(0, duration, int(sample_rate * duration))
freq = 440 # A4
sine_wave = np.sin(2 * np.pi * freq * t)
plt.plot(t[:1000], sine_wave[:1000])
plt.title('Sine Wave at 440 Hz')
plt.xlabel('Time (s)')
plt.ylabel('Amplitude')
plt.show()This Python code generates a 440 Hz sine wave using NumPy. The sample rate is 44.1 kHz, and the wave is plotted for the first thousand samples to show the waveform shape.
Quick Revision
- Sound is a pressure wave with frequency and amplitude determining pitch and loudness.
- Harmonics define timbre, the unique character of a sound.
- The ADSR envelope models how sound amplitude changes over time.
- Phase interference can cause cancellation; understanding it prevents audio issues.