# Physics Study Guide/Sound

## Intro

When two glasses collide we hear a Sound, when we pluck guitar string we hear a Sound

Different Sound generated from different sources . Generally speaking when two objects collides will result in a Sound

Sound does not exist in Vacuum . Sound needs medium's materials to travel .

Velocity of Sound wave depends on Temperature and the Pressure of the Medium . Sound travels at different speed in air, through water

# Sound

 $decibel(\mathrm{dB}) = 10\cdot \log\left(\frac{I_1}{I_0}\right)$
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 percieved 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/m2, 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), 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.

 $I_0 = 10^{-12} \mbox{ W}/\mbox{m}^2$

## Definition of terms

 Intensity (I): the amount of energy transferred through 1 m2 each second. Units: watts per square meter

 Lowest audible sound: I = 0 dB = 10-12 W/m2 (A sound with dB < 0 is inaudible to a human.) Threshold of pain: I = 120 dB = 10 W/m2

Sample equation: Change in sound intensity
Δβ = β2 - β1
= 10 log(I2/I0) - 10 log(I1/I0)
= 10 [log(I2/I0) - log(I1/I0)]
= 10 log[(I2/I0)/(I1/I0)]
= 10 log(I2/I1)
where log is the base-10 logarithm.

## Doppler effect

 $f' = f \, \frac{v \pm v_0}{v \mp v_s}$

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.

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