Musical acoustics is an ancient science - the rational approach to music was part of the ancient Greek quadrivium. As its name implies, this little book, Principles of Musical Acoustics, focuses on the basic principles in the science and technology of music.
The Source
An acoustic event consists of three phases as shown in Fig.1.1: First, the sound is generated by a source.
Transmission
Receiver
With respect to a fraction, the difference is in the numerator and one of the two quantities is in the denominator. For example, the sound of a guitar begins with the vibration of the strings, and the sound of a trumpet begins with the vibrations of the player's lips.
Mass and Spring
Definitions
Perhaps less obviously, the sound of the human voice begins with the vibration of the vocal cords (vocal cords), and the sounds that are reproduced electronically are ultimately converted into acoustic waves by the vibration of the speaker cone. Since sound begins with vibration, it is natural that the study of acoustics should begin with the study of vibration.
How It Works
The sine wave is periodic, so every two equivalent points in the waveform are separated in time by the time interval known as the "period". Theoretically, the sine wave extends indefinitely into infinite positive and infinite negative time, with no beginning or end. It is a time and is measured in seconds, or milliseconds (1 one-thousandth of a second).
Mathematical Representation
The argument of the sine function given by 360f tC here is an angle called the current phase. Panel (b) shows what happens if we take the sine of the angle and multiply it by the amplitude A.
Audible Frequencies
If an "infrasonic" sound has a frequency too low to be heard, what is "infrared". On the same set of axes, plot a sine wave with the same frequency and the same amplitude, but with an initial phase of 180ı.
Damping
This concept allowed us to define the terms used to discuss vibrating systems - terms such as amplitude and frequency.
Natural Modes of Vibration
Multimode Systems
The Tuning Fork
We are pretty sure that the frequency of the main mode of this tuning fork has not changed since Mozart's time. Mode shapes: The shapes of the main mode and the first timbre mode are shown in Fig.3.3.
The Spectrum
For an accurate plot, we can draw a series of vertical lines (fixed points in time) and plot a series of dots to show the sum of the waves. Then, by connecting the dots, we get the sum of the waves, as shown by the dashed line in part (c) of the figure.
Resonance
A Wet Example
Breaking Glassware
A crystal glass is a continuous system with many vibrational modes, but there is one main vibrational mode that is particularly important. As you can tell from the cup shot, this mode of vibration takes a long time to break down.
Sympathetic Strings
What happens to the frequency of the tuning fork when you file metal away from the tips of the teeth. What happens to the frequency if you file away metal near the intersection of the two teeth.
Transducers
The nineteenth century saw the beginning of a truly serious study of human hearing—anatomy, physiology, and psychology. This is the meaning of the word "linear". The idea of linearity also normally assumes that a straight line passes through the origin so that the output is zero when the input is zero.
The Oscilloscope
Analog ’Scope and CRT Display
When it controls the horizontal position of the point, the point always moves from left to right. This means that the horizontal movement of the point from left to right must sweep proportionally to time.
Digital ’Scopes and Liquid Crystal Displays
Then this voltage goes to the vertical amplifier of the oscilloscope to adjust its amplitude to a suitable value. In contrast to the analog CRT, which draws a continuous line, LCD uses a series of discrete pixels.
Beyond the Basic Oscilloscope
The Spectrum Analyzer
The analysis performed by the spectrum analyzer is much more complicated than simply displaying the signal on an oscilloscope. A digital spectrum analyzer can store a short signal in memory and later perform the frequency analysis.
The Frequency Counter
Obviously, a spectrum analyzer is just what we need if we want to analyze a signal into sinusoidal components. For example, if we give a signal from a tuning fork shortly after the beat, the spectrum analyzer will show the presence of amplitude at the main frequency and at the ringing mode frequency.
The Function Generator
36 4 Instrumentation Digital function generators are sometimes referred to as "waveform synthesizers". A waveform synthesizer allows the user to generate complicated waveforms of any shape, even transient waveforms. The transducers are driven by waveform synthesizers that simulate bumpy roads, potholes, potholes, etc. - anything that will torture a car and reveal weaknesses.
Virtual Instrumentation
What should you choose for the period of the sawtooth movement on the horizontal axis. When you are on the surface of the earth, you are under a sea of air.
Polarization
Transverse waves can exist in a medium if the medium has a certain resistance to bending. A longitudinal wave can exist in a medium if the medium has a certain resistance to compression.
The Speed of Sound
Supersonic Things
This is good because it provides a simple way to calculate the speed of sound for any normal air temperature. In reality, the speed of sound depends on the square root of the absolute temperature, referenced to absolute zero (273 µC).
Sound vs Light
It is an example of a mathematical technique commonly used in engineering and economics, linearizing a more complex function to represent behavior over a limited range.
Sound Waves in Space and Time
As this structure moves past point A, the speed at which the teeth or threads pass is equal to the speed of the structure divided by the distance. The length of time between the passage of freight cars is equal to the length of the cars divided by the speed of the train.
Sound Waves in More Than One Dimension of Space
The text says that the speed of sound at room temperature is 1,128 feet per second or 769 miles per hour. The speed of a sound wave in free air does not depend on the frequency of the wave.
Wave Addition
Interference
Note that if the extra travel time were a full period, then the waves from the two speakers would be in phase, and there would be completely constructive interference. Constructive interference occurs at all points where the distance from source A and the distance from source B differ by one wavelength, or two wavelengths, or three, etc., i.e.
Beats
The beat rate (the number of beats per second) is equal to the difference between the two frequencies. After 100 ms, the two waves 50 and 51 will have completed full cycles and will be in phase again.
Audio Analogies
As a result, the waves will be perfectly in phase again and there will be a maximum again. Ten beats per second is pretty fast, but you can still hear it as a rapidly changing volume.
Generalization
Wouldn't it be great if we could use electronics and the concept of interference to cancel out the noise around us. In fact, it is almost impossible with current technology to achieve active noise cancellation in a three-dimensional area of space, with the exception of longer wavelengths (lower frequencies).
Reflection
A specular reflection of sound waves in a room can lead to sound focusing - often leading to an uneven distribution of sound in the room.
Refraction
Diffraction
Segregation
You are 3 m away from one speaker and 3.4 m from the other. a) Find two values of the wavelength for which cancellation occurs. The added tone at 345 Hz has an amplitude somewhat smaller than the amplitude of the clear tone component at 350 Hz.
Standing Waves in General
Standing waves turn out to be the modes of vibration of important classes of musical instruments. If we look at the 500-Hz standing wave after another 0.25 ms (total time often5 D 1ms, or half the period), we find that it has changed from the original solid curve to the dashed curve in Fig.7.6.
Standing Waves on a String
Since the wavelength is twice the length of the string, the formula can be written as The other way the string oscillates has a perfect fit of the wavelength to the length of the string.
The Guitar Player’s Equation
To use the information from Eq. 7.2) and (7.6) together give the guitarist's equation for the fundamental frequency of a tone,.
The Stretched String: Some Observations
What is the frequency of the first (or fundamental) mode of oscillation if the speed of sound on the string is 154 m/s and the length of the string is 70 cm. From the guitarist's equation, Eq. 7.7), it looks as if the frequency of the guitar note, and thus its pitch, is entirely determined by the vibrating string and is in no way related to the body of the guitar.
Pipe with Both Ends Open
Pipe with One End Open and One End Closed
Playing a Pipe
80 8 Standing Waves in Tubes A shock that excites the tube's modals by striking the palm of the hand with the open end of the tube also excites all the modals. Again, all the frequencies of the different modes are present simultaneously, although the modes with the lowest frequency dominate.
Thinking Critically
Open-End Corrections
You close one end of the tube and blow through the open end again. In what way the final correction depends on the ratio of pipe diameter to pipe length.
The Sine Wave
Complex Waves
Periodicity
The two components can be seen in the amplitude and phase plots to the right. This phase change causes a change in the waveform, but does not cause a change in the sound of the waveform.
The Sawtooth
90 9 Fourier analysis and synthesis waveform, and then we expect the sine wave components to be harmonic. The fundamental has an amplitude of 1, the second harmonic has an amplitude of 1/2, the third harmonic has an amplitude of 1/3, and so on.
The Sounds
The fact that this simple sine waveform, with only a single component, can have a tonal color that spans the range from dull to piercing tells you that the color of a note depends more on the frequencies present in that note than of the shape of the waveform. For a typical complex tone, the fundamental frequency (reciprocal of the period) determines the pitch, and the amplitudes of the components determine the timbre or steady-state timbre of the tone.
Harmonic and Inharmonic Spectra, Periodic
You may have asked yourself, "What's the point of this Fourier analysis?" "Who cares if a waveform like a sawtooth or whatever can be analyzed into components of different frequencies, or synthesized by adding sine tones at those frequencies?" Ultimately, the answer to these questions is filtering. 9.8(a) A computer code (ASCII) for the letter "Y". (b) The computer signal from (a) after passing through a channel with a bandwidth of only 0.8 MHz. c) The computer signal of (a) after passing through a channel with a bandwidth of 4.0 MHz.
Continuous Spectra
The discussion of phase-scrambled sawtooth in the text says that the sawtooth waveform has a pitch of 400 Hz. Božo explains that according to Ohm's law, the amplitude spectrum determines the shape of the waveform.
Pressure, Power, and Intensity
100 10 Intensity of sound Note that this means that if the pressure is doubled, the intensity is quadrupled. If the pressure increases by ten times, then the strength increases by 100 times, that is, it increases by a factor of 100.
The Inverse Square Law
Therefore, the intensity of the sound wave measured a distance from the source is I DP =.4d2/, where. Application of the inverse square law The inverse square law comes from a model in which there is a source, a receiver and nothing but air.
Decibels
The inverse square law applies to the propagation that occurs at each step of this complex path. Therefore, we could instead say, "The sound level is 60 dB relative to the hearing threshold."
Absolute vs Relative dB
The level of the Chevrolet horn (C) is 5 dB greater than the level of the Ford horn (F). Physiology begins with anatomy—the science of where things are in the body, what they look like, how they fit together, and how these facts provide clues to physiological function.
Auditory Anatomy
- The Outer Ear
- The Middle Ear
- The Inner Ear
- The Semicircular Canals
Changes in ion concentration provide the energy source for hair cell action. However, the semicircular canal mechanism is only sensitive to low frequencies of whole head movement, mostly below 10 Hz.
Auditory Function
- Outer Ear Function
- Middle Ear Function
- Inner Ear Function
- Beyond the Cochlea
- Hearing Impairments
The basilar membrane is caused to vibrate by the vibrations of the fluids in the cochlea. Fortunately, in the case of the cochlea there is a multi-pronged approach that has been successful.
Loudness Level
The experiment begins when the experimenter presents a sine tone with a frequency of 1,000 Hz and some chosen level, e.g. 20 dB. In this example, where the sound level of 1,000-Hz sine is 20 dB, it is found that the sound level of 125-Hz sine must be adjusted to 33 dB for the same volume.
Loudness
Given the relationship in Eq. 12.6) it follows that if there are two tones of the same frequency with levels L1 and L2, the loudnesses are related to the ratio. This statement comes close to saying that loudness increases as the cube root of intensity.
Psychophysics
This time the experimenter gives the listener the numbers, and the listener adjusts a volume control to change the intensity of the sound. If the listener had previously given numbers on a scale of 1-100 in the estimation task, the experimenter would give the listener the same range of numbers for the production task.
Neural Firing Rate
Excitation Patterns
Not only do active neurons become more active (eg, the neuron at location B), but additional neurons (eg, the neuron at location A) begin to fire outside their spontaneous rate. The additional spikes contributed by the neuron at A will help somewhat to generate the loudness sensation when the neurons near location B are saturated.
Complex Sounds
The neurons that respond to the narrow band of noise are essentially the same neurons that will respond to a sine tone and we feel confident about using the entire sine-tone model to calculate the loudness of a narrow-band noise . So if one tone has an intensity of 2 units and the other tone has an intensity of 3 units, the loudness will be proportional to.2C3/0:3D50:3 or 1.62.
Critical Band
In terms of the equal loudness contours, why is it said that the threshold of hearing is 0 dB. The most important physical correlate of the psychological sensation of pitch is the physical property of frequency, and our acute perception of pitch allows us to make fine distinctions along a frequency scale.
Pitch of Sine Tones: Place Theory
Pitch: Timing Theory
Pitch of a Complex Tone
Place theory might predict that a tone with ten harmonics, as in Figure 13-2, should lead to ten different pitches. But before we give up on the theory of places, we need to do some experimentation.
The Template Theory
Compared to the actual components, the sample fourth harmonic would be too low (824 < 830), the sample sixth harmonic would be too high (1; 236 > 1; 230), and the sample fifth harmonic would be just right. It can be argued that if we insist on the harmonic proposal, then 206 Hz leads to the best match with the three components actually present.
Pitch as an Interpretative Percept
Absolute Pitch
When you're done, you'll have created an interspike interval histogram—a very useful representation used every day by neuroscientists. The processes are different depending on where the sound happens to be in relation to your head.
Horizontal Plane
Interaural Level Differences
It is not difficult to show that unless a sound source is very close to your head, the distance effect is not important. But the distance effect is clearly important when the source is very close to your head, for example when there is a mosquito in one of your ears.
Interaural Time Differences
Then, the binaural system can only register time differences in the envelope (ie amplitude), including the onset. The sections above describe horizontal (azimuth) plane localization for steady-state sounds—continuous portions of sine tones or complex tones with a simple spectral structure and no sudden onset.
Localization in the Vertical Median Plane
For tones above the not particularly high frequency of 1,400 Hz, ILD has the main influence on localization, although some additional information is available in ITD when modulating a time-varying signal, as shown in segment (2) of Figure 14.4. The utility of ITD and ILD in sine tones is unusually frequency dependent.
The Precedence Effect
The precedence effect is particularly easy to study with a click pair, as shown in Figure 14-5. Click pairing experiments have highlighted that the precedence effect depends significantly on high levels of the central nervous system.
Perceived Auditory Space
If the same interaural differences are produced using headphones, the image will be lateralized approximately halfway between the center of the head and the extreme right. These anatomical features leave their own distinctive mark on the frequency content of broadband sounds such as bursts of noise as a function of the relative location of the source.
Reflections from a Surface
The study of sound in the environment begins by thinking about the different ways that sound can travel from a source to a receiver. The most important assumption in the approximation is that the surface itself (whether smooth or rough) is large relative to the wavelength of the sound.
Transmission Loss
Specular reflection occurs when the surface is smooth, with bumps that are small compared to the wavelength of the sound. Diffuse reflection occurs when the bumps on the surface are comparable to the wavelength or larger.
Room Acoustics
Early Reflections in a Room
Reflections that arrive within the first 20 ms give a sense of intimacy to the acoustic environment. Reflections from the ceiling contribute favorably to noise, but they do not lead to the same sense of space.
Focused Sound
In part (a) the rays are concentrated at a point causing the intensity to be large there. In part (b) the rays are spread widely, helping to create an even distribution of sound intensity.
Reverberation
The Sabine equation It is possible to estimate the reverberation time from a few simple physical properties of the room. Because excessive reverberation makes speech difficult to understand, you can imagine that the ideal speech-only classroom or auditorium would have no reverberation at all, ie. the reverberation time would be zero.
Gaining Control of Acoustical Spaces
The computer also needs data on the absorption coefficients of the materials chosen by the architect. The surfaces in room B are made of the same materials as the corresponding surfaces in room A.
Basic Definitions
An electric current occurs when electrons move preferentially in one direction, such as from one end of a copper wire to the other. With a voltage present, either steadily from a battery or alternating from an electrical signal, a current flows.
The Current and Magnetism Principle
Application of the Current–Magnetism Principle
The electrical signal is amplified and sent to a coil that produces a magnetic field in the record head, due to the current–. The magnetic field in the gap leaves a residual field on the tape, a permanent record of the signal at a specific time as shown in Fig.16.4.
The Analog Concept
The Generator Principle
The movement of the diaphragm caused by the pressure in the acoustic wave causes the coil to move in the magnetic field. This relative motion causes a voltage to be induced in the coil. waves) causes the diaphragm to move outward and this change produces a negative voltage.
The Motor Principle
The generator principle is also responsible for the operation of the phonograph cartridge used to play vinyl records.
Electrostatic Devices
The best microphones are used in recording studios; the cheapest microphones are used in telephones and mobile phones and for speech input to computer sound cards. The cheapest microphones are electret microphones where the polarizing voltage comes from special materials that have a fixed charge, which creates a fixed electrostatic field just as a permanent magnet creates a fixed magnetic field.
Electro-Optical Transducers
When the light beam hits the "ground" (the flat area between the dimples), the beam is strongly reflected. If you had to design a microphone, you would attach it to the diaphragm - a coil or a permanent magnet.
Noise
Distortion
Distortion Not
Linear Distortion
Consequently, the output waveform is smoother than the input - linear distortion. e) The output of a filter that introduces phase distortion. The high-frequency harmonics are just as strong as in the input sawtooth, but their phases have changed, changing the shape of the waveform: linear distortion. f) The output of a time delay device - no distortion. G).
Nonlinear Distortion
The tone remains periodic because each cycle of the sine tone's top is clipped in the same way. If the non-linear system cuts off the top and bottom of the sine tone symmetrically, as in Fig.
Dynamic Range
Compare with the ratios in Appendix D to determine the musical interval in the car horn sound. Can you account for all the peaks in the spectrum assuming they are harmonics. e).
Sound Recording
The purpose of this chapter is to identify some concepts and terms that describe audio systems. Arguably, reinforcing the concept that all the sounds we hear at once actually add up to a single waveform is the most important philosophical contribution of sound recording.
Public Address System
Preamplifier
On the front of the preamplifier is a switch that allows the user to select one of the sources. Of the modern preamplifier inputs listed above, only PHONO is a low voltage input that requires a lot of voltage gain.
Power Amplifier
Mixer
Tone Controls and Equalizers
Dynamic Range Compressor
Integrated Amplifiers
Receiver
More Integration
Multichannel Audio
Loudspeakers: What We Want
The Two-Way Speaker
Enclosures
More About Loudspeaker Diffusion
Powered Speakers
Subwoofers
Digital vs Analog
Digital Noise
Sampling
Contemporary Digital Audio
Continuous Wave
Amplitude Modulation
Frequency Modulation
Bandwidth
Carrier Frequencies
Vocal Anatomy
Voiced Sounds
Speech Sounds
Spectrograms
Sustained-Tone Instruments
Evolution of the Resonances of a Trumpet
Tone Production: Feedback and Nonlinearities
Single-Reed Instruments
Double Reeds
Reeds in General
Edge Tone Instruments
Boatswain’s Pipe
The Flute
Percussive Strings
The Guitar
The Electric Guitar
The Piano
Bowed Strings
Tone Generation in the Bowed Strings
The Violin Body
Bars, Rods, and Tubes
Useful Bars
Useful Tubes
Membranes
Chladni Patterns
Timpani
Plates: Cymbals, Gongs, and Bells
Nonlinear Mode Coupling
Bells
Analog Synthesizers
Digital Synthesizers
Musical Instrument Device Interface
