Introduction To Sound

Front 1

What is Sound?

Back 1

-Vibrations propagated through a medium.
-Any elastic medium (water, metal, wood, air)
will propagate sound.
-Sound canʼt travel in a vacuum.

Front 2

Sound propagation

Back 2

Sound in air involves dynamic variations in air pressure, due to CONDENSATION (high pressure) and RAREFACTION (low pressure) of air molecules.

Front 3

Rate or Frequency

Back 3

A change in rate of vibration changes the frequency and wavelength of the sound.

Front 4

SHM and the circle

Back 4

The height of the dot at any point in time is the sine of the angle between the 0 degree line and the line connecting the dot and the center.
This is why is it called sinusoidal motion.

*SHM: F is proportional to distance from center

Front 5

A sinusoid is completely described by:

Back 5

– Period (T) in seconds per cycle.
– Peak Amplitude (A)
– Phase (φ) in radians

Front 6

Why Sinusoids?

Back 6

Sinusoids form the building blocks of all sounds in our environment.

• Any sound (or waveform) can be described as the sum of (many) sinusoids, each with a different amplitude, frequency, and phase.

Front 7

Typical Hearing Range:

Back 7

20 Hz – 20,000 Hz

Front 8

Range of musical notes:

Back 8

27.5 Hz to 4186 Hz
(modern grand piano)

Front 9

Wavelength

Back 9

Snapshot at one point in time

Front 10

Period

Back 10

View at one point in space

Front 11

Period and frequency relationship

Back 11

• Period (seconds per cycle) is the inverse of
Frequency (cycles per second): T = 1/f

Front 12

Period and the speed of sound

Back 12

Wavelength depends on the Period and the speed of sound: λ = cT
Therefore: λ = c/f

Front 13

What happens if two sinusoids of the same
frequency and amplitude are added?

Back 13

You always end up with the same frequency

Front 14

Constructive Interference

Back 14

is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction

Front 15

Destructive Interference

Back 15

is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction

Front 16

Quantities and Relationships

Back 16

• 1000 Hz = 1 kHz = 1000 cycles per second
• 1 ms = (1/1000) s = 10-3 s = 1 millisecond
• If the frequency is 1000 Hz, then the period is:
(1/1000) s = 1 ms

Front 17

What is the frequency if the period is 2 ms?

Back 17

1/2000= 2ms; 2000Hz

Front 18

What is the period if the frequency is 10 Hz?

Back 18

1/10= 0.1 s

Front 19

The Decibel Scale

Back 19

• A factor of one million million difference
between the quietest audible and loudest
bearable sound.
• The decibel scale helps to keep numbers more
manageable.

Front 20

140 dB

Back 20

Jet aircraft at take-off (30 m away)

Front 21

120dB

Back 21

Rock concert

Front 22

90dB

Back 22

Cocktail party

Front 23

60dB

Back 23

Conversational speech

Front 24

30dB

Back 24

Whispered speech

Front 25

0dB

Back 25

Hearing threshold at medium frequencies

Front 26

Typical range for a
radio pop music
broadcast

Back 26

30-90dB

Front 27

Spectral Analysis

Back 27

Sinusoids can be represented by their frequency and amplitude (and phase).

Fourier Transform:

Time domain--> Fourier transform--> Frequency domain (amplitude spectrum)

Front 28

Harmonic complex tones

Back 28

• These tones form the basis of nearly all musical sounds (as well as voiced speech).
• All frequency components are multiples of the
fundamental frequency.
• The waveform of the tone repeats at the period of the fundamental frequency.

Front 29

Resonance/resonant frequency

Back 29

• Most objects have a frequency that they best respond to.
– Wine glass
– Ruler on the edge of table
– Mass on end of spring
• is vital for all musical instruments.
• is determined by: Mass, and Stiffness

Front 30

What happens to resonant frequency
(f0) if stiffness is increased?

Back 30

f0 increases

Front 31

What happens to resonant frequency
(f0) if mass is increased?

Back 31

f0 decreases.

Front 32

Resistance (or damping) reduces the
amplitude of vibration at resonance.
Changing the amplitude does not
change the resonant frequency.

Back 32

high damping: low amplitude

low damping: high amplitude

Front 33

Filters

Back 33

This changes the spectrum of a sound by attenuating some frequencies relative to others.

*low-pass --\ (low freq: 500Hz), band-pass, and high pass /-- (high freq: 5000Hz)*

Front 34

Filtered Noise: White noise

Back 34

has equal energy at all frequencies (on average)

Front 35

*The sound of musical instruments and voices can be understood in terms of a source and filter:

1. Speech

2. Music

Back 35

1. Sound from Vocal Folds --> Resonances in vocal tract=

2. String--> Guitar=

Front 36

Timbre

Back 36

– “Brightness” or “sharpness” determined by the spectral “center of gravity” of a sound.

-Higher frequencies produce brighter sound.
– Low-frequency components produce “deep”, “rich” sound

Energy in the mid-frequencies (around 2 kHz) thought to add “presence”.

Front 37

What determines sound
quality (vowel or instrument)?

Back 37

Pattern of peaks and dips in spectrum

Front 38

Spectrum ≠ Timbre

Back 38

-Most musical instruments recognizable even after severe spectral distortions.
-Temporal envelope has large effect on timbre.

-different harmonics rise and fall at different times

Front 39

Reflected (reverberant) sound:

Back 39

– Sound bouncing off one or more surfaces before reaching ear.

*Amount of reflected energy depends on absorption of the walls.*
– Highly reflective surfaces (stone, glass, etc.) can lead to long reverberation;
– Highly absorptive materials (cloth, foam, etc.) lead to much shorter reverberation.

Front 40

“Reverberation Time” or RT60

Back 40

• This is the time taken for sound to decay by 60 dB, or a factor of 1,000,000 in intensity.
• Energy at different frequencies can decay at different rates.

Front 41

Advantages of reverberation:

Back 41

– Sustains sound
– Increases volume
– Provides sense of “spaciousness”

Front 42

Disadvantages of reverberation:

Back 42

– Smears sound
– Reduces speech intelligibility
– Reduces ability to localize sound

*Different music styles require different reverberation times

Front 43

Distortion

Back 43

non-faithful reproduction of original
sound

Front 44

Linear Distortion

Back 44

changing the spectral shape, but not changing the frequencies present (e.g., filtering)

Front 45

Nonlinear Distortion

Back 45

changing the spectral content

Front 46

In music, the most common form of distortion

Back 46

is to push an amplifier into saturation