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## Sound

Science topics

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### Sound

Sonic spectrum: frequency range for ALL longitudinal waves

Lower Frequency Limit    |    Audible Range                             |        Upper Frequency Limit
no actual lower limit |            for humans 20 Hz - 20,000 Hz |        depends on spacing of particles |
earthquake f ~ 1 × 10–3 Hz |                                                       in gases, ~ 1 × 109 Hz

Sound: the range of frequencies to which the human ear is sensitive

*infrasonic: frequencies < 20 Hz
*ultrasonic: frequencies > 20,000 Hz

In air, the speed of sound depends on density, air pressure, and temperature.

At 0°C, V = 331.5 m/s

The speed of sound increases by 0.6 m/s for every °C of temperature increase

V = 331.5 m/s + (0.6 m/s/°C)(T)
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### Re: Sound

 Physical Property1. intensity2. frequency3. harmonic content Interpreted asloudnesspitchquality (timbre)

INTENSITY
Intensity: the rate of energy transfer (power) per unit area

I = P/A

The intensity of a wave decreases the farther it is away from the source because the area increases.
The power passing through a sphere of one radius is the same as the power passing through a sphere of another radius.

Compare two intensities as a ratio:
I[sub]1[/sub]r[sub]1[/sub]2 = I[sub]2[/sub]r[sub]2[/sub]2

Intensity → Loudness
Threshold of hearing - the absolute lowest intensity sound that the human ear is capable of detecting. At 1000 Hz, this corresponds to 1 × 10–12 W/m2

Threshold of pain - the highest intensity that the human ear can withstand without pain. At 1000 Hz, this corresponds to 1 W/m2.

The perceived loudness is not directly proportional to the intensity. A sound with twice the intensity will not be perceived as twice as loud.
The doubling of perceived loudness corresponds to an increase in intensity of 10 times.

INTENSITY LEVEL
• Uses a logarithmic scale to express the large range of intensities
• Must be referenced to a standard intensity - typically we use the threshold of hearing 1 × 10–12 W/m2
• Typically measured in decibels (dB), which is a tenth of a Bel
• Is ten times the logarithm of the ratio of two intensities: Δβ = $10\log(\frac{I_1}{I_2})$
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### Re: Sound

Frequency → Pitch

higher frequency → higher pitch

The Superposition Principle:
When two or more waves travel through the same medium,
1. Each wave proceeds independently as if no other wave was present.
2. The resultant displacement of any particle at a given time is the vector sum of the displacements caused by each individual wave.

BEAT FREQUENCY
When two sounds interfere that are close in frequency but not the same, an interference pattern results that yields varying intensities and that can be perceived as a pulsing sound.
The oscillation of intensity is called a beat.

beat frequency -- # of beats per second
f[sub]B[/sub] = |f[sub]2[/sub] – f[sub]1[/sub]|
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### Re: Sound

Doppler Effect
the variation of the perceived frequency associated with the relative motion between a sound source and a listener

If the SOURCE is moving:
$f'=\frac{f}{1\mp \frac{V_s}{V}}$

f: frequency of source
f': observed frequency
V[sub]s[/sub]: velocity of source
V: wave speed (speed of sound) → 343 m/s

If the source is moving TOWARDS the observer, the observer will hear a higher frequency, so use "–"

If the OBSERVER is moving:
$f'=f(1\pm\frac{V_o}{V})$

V[sub]o[/sub]: velocity of observer

If the observer is moving TOWARDS the source, add.
If it's moving AWAY, subtract.
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