16.6 The Speed of Sound• Sound travels through gases, liquids, and

solids at different speeds.• Room temperature: speed of sound in air

is 343 m/s (767 mi/h) and greater in liquids and solids.

• Sound travels more than four times faster in water and more than seventeen times faster in steel than it does in air.

• Sound travels slowest in gases, faster in liquids, and fastest in solids.

• Issac Newton was the first to measure sound.

• http://www.youtube.com/watch?v=PzUU4G4uW18&feature=related

Sound in a gas

• Only when molecules collide that the condensations and rarefactions of a sound wave can move from place to place.

• Speed of sound in a gas to have the same order of magnitude as the average molecular speed between collisions.

Speed in Ideal Gas• Translational rms (root mean square) speed given

in the following equation14.6

T = KelvinM = massk = Boltzmann’s constant (relation between absolute

temp. and the KE contained in each molecule of an ideal gas)

Overestimates the speed of sound. It gives the correct dependence on Kelvin temperature and particle mass.

Speed of sound in an ideal gas(16.5)

y = cp/cv ratio of specific heat capacity at constant pressure cp to the specific heat capacity at constant volume cv. (adiabatic)

Ideal monatomic gas: y = 5/3 (atoms are not bonded together)

Y = 7/5 for ideal diatomic gases (composed of 2 atoms)

Y is here because the condensations and rarefactions of a sound wave are formed by adiabatic compressions (impassable) and expansions of the gas.

Example 4: An Ultrasonic Ruler

Practice Problem 44

Homework

• Pg. 506• Ques. 29, 30, 31

Sonar• Sound navigation ranging• Used to determine water depth and locating

underwater objects, such as reefs, submarines, and schools of fish.

• Ultrasonic transmitter and receiver mounted on the bottom of a ship.

• Transmitter emits a short pulse of ultrasonic sound, later the reflected pulse returns and is detected by the receiver.

• Depth determined the time it took for the sound to return. http://www.youtube.com/watch?v=Xc2EZjG0b8U&feature=related

Liquids

• In a liquid, the speed of sound depends on the density p and the adiabatic bulk modulus Bad of the liquid:

(16.6)

Liquids

• Adiabatic bulk modulus Bad (substance's resistance to uniform compression) is used when calculating the speed of sound in liquids.

• In seawater sound is 1522m/s (4x greater than in air).

In Medicine• Ultrasonic probe called an A-scan is used

to measure the length of the eyeball in front of the lens, thickness of the lens, and the length of the eyeball between the lens and the retina.

• Needed information is the speed of sound in the material in front of and behind the lens of the eye is 1532m/s and that within the lens is 1641m/s.

Solid Bars

• When sound travels through a long slender solid bar, the speed of the sound depends on the properties of the medium according to

16.7 Sound Intensity

• Sound waves carry energy that can be used to do work.

• Sonic boom: can carry enough energy to cause damage to windows and buildings.

• The amount of energy transported per second by a sound wave is called the power of the wave and is measure in SI units of joules per second (J/s) or watts (W).

• http://www.youtube.com/watch?v=QX04ySm4TTk&feature=related

• http://www.youtube.com/watch?v=k-Um5EiaAxo&feature=related

• http://www.youtube.com/watch?v=PMg_nd-O688

Sound Intensity I

• Power spreads out as it leaves the source.• It spreads out but has the same power

even when spread out over a greater area.• Sound Intensity I: sound power P that

passes perpendicularly through a surface divided by the area A of that surface:

Example 6: Sound Intensities

• The sound intensity is less at the more distant surface, where the same power passes through a threefold greater area. The ear of a listener, with its fixed area, intercepts less power where the intensity, or power per unit area, is smaller. Thus listener 2 intercepts less of the sound power than listener 1. With less power striking the ear, the sound is quieter.

Threshold of Hearing

• For a 1000Hz tone, the smallest sound intensity that the human ear can detect is about 1x10^-12W/m2. (threshold of hearing)

• Intensities greater than 1 W/m2 can be painful and result in permanent hearing damage if continuously exposed to them.

• A source emits sound uniformly in all directions, the intensity depends on distance.

• If the source is at the center of an imaginary sphere. The radius of the sphere is r. Since all the radiated sound power P passes through the spherical surface of A = , the intensity at a distance r is.

Example 7: Fireworks

16.8 Decibels