# Physics Study Guide/Sound

Sound is defined as mechanical sinosodial vibratory longitudinal impulse
waves which oscillate the pressure of a transmitting medium by means of
adiabatic compression and decompression consequently resulting in the
increase in the angular momentum and hence rotational kinetic energy of
the particles present within the transmitting medium producing
frequencies audible within hearing range, that is between the threshold
of audibility and the threshold of pain on a Fletchford Munson equal
loudness contour diagram.

## Intro

When two glasses collide, we hear a sound. When we pluck a guitar
string, we hear a sound.

Different sounds are generated from different sources. Generally
speaking, the collision of two objects results in a sound.

Sound does not exist in a vacuum; it travels through the materials of a
medium. Sound is a longitudinal wave in which the mechanical vibration
constituting the wave occurs along the direction of the wave\'s
propagation.

The velocity of sound waves depends on the temperature and the pressure
of the medium. For example, sound travels at different speeds in air and
water. We can therefore define sound as a mechanical disturbance
produced by the collision of two or more physical quantities from a
state of equilibrium that propagates through an elastic material medium.

# Sound

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`<big>`{=html}**$decibel(\mathrm{dB}) = 10\cdot \log\left(\frac{I_1}{I_0}\right)$**`</big>`{=html}

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thumb\|400px\|right\|Fig. 1: The Fletcher-Munson equal-loudness
contours. Phons are labelled in
blue. The amplitude is the
magnitude of sound pressure change within a sound wave.
Sound amplitude can be measured in pascals (Pa),
though its more common to refer to the *sound (pressure) level* as
Sound intensity(dB,dBSPL,dB(SPL)), and
the *perceived sound level* as Loudness(dBA,
dB(A)). **Sound intensity** is flow of sound energy per unit time
through a fixed area. It has units of watts per square meter. The
reference Intensity is defined as the minimum Intensity that is audible
to the human ear, it is equal to 10^-12^ W/m^2^, or one picowatt per
square meter. When the intensity is quoted in decibels this reference
value is used. **Loudness** is sound intensity altered according to the
frequency response of the human ear and is measured in a unit called the
A-weighted decibel (dB(A) "wikilink"), also used to be called
phon).

## The Decibel

The decibel is not, as is commonly believed, the unit of sound. Sound is
measured in terms of pressure. However, the decibel is used to express
the pressure as very large variations of pressure are commonly
encountered. The decibel is a dimensionless quantity and is used to
express the ratio of one power quantity to another. The definition of
the decibel is $10\cdot \log_{10}\left(\frac{x}{x_0}\right)$, where x is
a squared quantity, ie pressure squared, volts squared etc. The decibel
is useful to define relative changes. For instance, the required sound
decrease for new cars might be 3 dB, this means, compared to the old car
the new car must be 3 dB quieter. The absolute level of the car, in this
case, does not matter.

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| `<big>`{=html}**$I_0 = 10^{-12} \mbox{ W}/\mbox{m}^2$** `</big>`{=html} |
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| </center>                                                               |
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+-------------------------------------------------------------------------+

## Definition of terms

+----------------------------------------------------------------------+
| **Intensity (I):** the amount of energy transferred through 1 m^2^   |
| each second. Units: watts per square meter\                          |
| \                                                                    |
+----------------------------------------------------------------------+

+----------------------------------------------------------------------+
| **Lowest audible sound:** I = 0 dB = 10^-12^ W/m^2^ (A sound with dB |
| \< 0 is inaudible to a human.)\                                      |
| \                                                                    |
| **Threshold of pain:** I = 120 dB = 10 W/m^2^                        |
+----------------------------------------------------------------------+

*Sample equation:* **Change in sound intensity**\
Δβ = β~2~ - β~1~\
= 10 log(*I*~2~/*I*~0~) - 10 log(*I*~1~/*I*~0~)\
= 10 \[log(*I*~2~/*I*~0~) - log(*I*~1~/*I*~0~)\]\
= 10 log\[(*I*~2~/*I*~0~)/(*I*~1~/*I*~0~)\]\
= 10 log(*I*~2~/*I*~1~)\
where log is the base-10 logarithm.

## Doppler effect

+------------------------------------------------------------------------+
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| `<big>`{=html} $f' = f \, \frac{v \pm v_0}{v \mp v_s}$ `</big>`{=html} |
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| ```{=html}                                                             |
| </center>                                                              |
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+------------------------------------------------------------------------+

\
f\' is the observed frequency, f is the actual frequency, v is the speed
of sound ($v=336+0.6T$), T is temperature in degrees Celsius $v_0$ is
the speed of the observer, and $v_s$ is the speed of the source. If the
observer is approaching the source, use the top operator (the +) in the
numerator, and if the source is approaching the observer, use the top
operator (the -) in the denominator. If the observer is moving away from
the source, use the bottom operator (the -) in the numerator, and if the
source is moving away from the observer, use the bottom operator (the +)
in the denominator.

### Example problems

A. An ambulance, which is emitting a 400 Hz siren, is moving at a speed
of 30 m/s towards a stationary observer. The speed of sound in this case
is 339 m/s.

$f' = 400\,\mathrm{Hz} \left( \frac{339 + 0}{339 - 30} \right)$

B. An M551 Sheridan, moving at 10 m/s is following a Renault FT-17 which
is moving in the same direction at 5 m/s and emitting a 30 Hz tone. The
speed of sound in this case is 342 m/s.

$f' = 30\,\mathrm{Hz} \left( \frac{342 + 10}{342 + 5} \right)$
