CH 14 Sections (3-4-10) Sound Wave

Sound is a wave (sound wave) Sound waves are longitudinal waves: longitudinal wave the particle displacement is parallel to the direction of wave propagation.

They have the frequency range 20 Hz to 20,000 Hz, the normal range of human hearing. They can travel through any material, except vacuum.

14.3 The Speed of Sound The speed of sound depends on the properties of the substance through which the wave is travelling. It is variable in various media. The speed of a sound wave in a fluid depends on the fluid’s compressibility and density.

The Speed of Sound in fluid If the fluid has a bulk modulus B and an equilibrium density ρ, the speed of sound in it is:

The Bulk Modulus (B) It describes the amount of pressure that need to be applied to the body for a known change in volume. the ratio of the change in pressure to the resulting fractional change in volume, = - ∆P/ (∆V/V) B is always positive because the ratio (∆P/∆V) is always negative because an increase in pressure results in a decrease in volume. Its SI unit is the Pascal.

Approximate bulk modulus for other substances: Water : 2.2×109 Pa ) Air: 1.42×105 Pa

Speed of sound in solids In general, the speed of sound v in solid rod which is given by this equation : Where: Y is the Young's modulus of the solid. ρ is the density of the solid. This expression is valid only for a thin, solid rod.

Sound mediums In general, sound travels faster through solids than liquids and faster through liquids than gases The speed of sound is much higher in solids than in gases because the molecules in a solid interact more strongly with each other than do molecules in a gas.

The Speed of Sound in the air and Temperature The speed of sound also depends on the temperature of the medium. Molecules at higher temperatures have more energy, thus they can vibrate faster. Since the molecules vibrate faster, sound waves can travel more quickly.

For sound traveling through air, the relationship between the speed of sound and temperature is: The Speed of Sound in the air

Ex 14.1 P 463: An explosion occurs 275 m above an 867-m-thick ice sheet that lies over ocean water. If the air temperature is -7.00°C, how long does it take the sound to reach a research vessel m below the ice? Neglect any changes in the bulk modulus and density with temperature and depth. (Speeds of Sound in sea water= 1533, Bice = 9.2 *10 Pa)? 1.93 s

14.4 Energy and Intensity of Sound Waves Sound intensity (I):The amount of energy that is transported past a given area of the medium per unit of time is known as the intensity of the sound wave.

Sound intensity level (β) β= 10 log (I/I 0 ) Where: β : Intensity Level in Decibels I 0 : the reference intensity= 1 x I : the intensity

Intensity of Sound Waves is defined as the sound power P per unit area A. I = P / A. Where: I is the sound intensity. P is the sound power P. A is the surface area. S.I unite watt per meter squared.

EXAMPLE A noisy grinding machine in a factory produces a sound intensity of 1.00 x W/m 2 Calculate (a) the decibel level of this machine? (b) the new intensity level when a second, identical machine is added to the factory. (c) A certain number of additional such machines are put into operation alongside these two machines. When all the machines are running at the same time the decibel level is 77.0 dB. Find the sound intensity.

a)70.0 dB b)73.0 dB c) 5.00 x 10-5 W/m2

14.8 Standing Waves When a wave moves along a string, we say the wave is propagating along the string, as shown. When the end of string is fixed, the wave gets reflected.

Standing Waves can occur when a wave interferes with its reflected self. Standing waves result when two waves trains of the same frequency are moving in opposite directions in the same space and interfere with each other. Such as sound waves reflected from a wall.

Superposition principle: If two or more traveling waves are moving through a medium, the resultant value of the wave function at any point is the algebraic sum of the values of the wave functions of the individual waves. The incident and reflected waves combine according to the superposition principle.

There are two main parts of the standing wave: 1- Node : A node occurs where the two traveling waves have the same magnitude of displacement but the opposite sign, so the net displacement is zero at that point. Points of complete destructive interference. There is no motion in the string at the nodes. Parts of the Standing Wave

2- an anti-node: The opposite of a node. A point where the amplitude of the standing wave is a maximum. These occur midway between the nodes.

Consider a string of length L that is fixed at both ends, In our case, we have strings with nodes at both ends, which produces the following: The Relationship between the Wavelength and the Length of the String

The ends of the string must be nodes, because these points are fixed. If the string is displaced at its midpoint and released, the vibration shown in Active. Since each loop is equivalent to one-half a wavelength,

where n is an integer representing the harmonic number. So: The Relationship between the Wavelength and the Length of the String:

The Fundamental frequency or First Harmonic

The Second Harmonic

The Third Harmonic

Natural frequencies of a string fixed at both ends

Example (1) Finding the wave speed on the string of the fundamental harmonics when L0 = m and f1 = 329 Hz?

EXAMPLE 14.8 (a)Find the frequencies of the fundamental,second, and third harmonics of a steel wire 1.00 m long with a mass per unit length of 2.00*10-3 kg/m and under a tension of 80.0 N. (b) Find the wavelengths of the sound waves created by the vibrating wire for all three modes. Assume the speed of sound in air is 345 m/s?

14.10 Standing Waves in Air Columns 1- Pipe open at both ends all harmonics are present: Where: v is the speed of sound in air.

2-Pipe closed at one end (only odd harmonics are present):

EXAMPLE 14.9 A pipe is 2.46 m long. (a) Determine the frequencies of the first three harmonics if the pipe is open at both ends. Take 343 m/s as the speed of sound in air. (b) How many harmonic frequencies of this pipe lie in the audible range, from 20 Hz to Hz? (c) What are the three lowest possible frequencies if the pipe is closed at one end and open at the other?