Sound

• Characteristics of sound waves

• The motion of the elements of the medium in a longitudinal sound wave is back and forth along the direction which the wave travels

• In transversal wave, the vibration of the elements of the medium are at right angles to the direction of travel of the wave\

• Sound waves: audible waves, infrasonic waves( earthquake), ultrasonic wave

• The speed of sound• v=√B/ρ; • b- bulk modulus of the fluid B=ΔP/(ΔV/V)• For a speed of transverse wave on a string

v=√F/μ• The speed of mechanical wave:

v=√elastic property/inertial property• Speed of longitudinal wave in a solid rod

v=√Y/ρ; Y-young’s modulus• Relationship between speed of sound and

temperature : v=(331 m/s)√T/273K

• Energy and Intensity of sound waves

• The average intensity T of a wave on a given surface is defined as the rate at which energy flows through surface ΔE/Δt, divided by the surface area: I=1/A(ΔE/Δt), where the direction of energy flow is perpendicular to the surface at very point

• SI unit: W/m2

• I=power/area =PP/A

• The relative intensity of a sound is called the intensity level or decibel level β=10 log (I/Io)

• The Doppler effect (is associated with sound, but its common to al waves, including light)

• #1 The observer is moving relative to a stationary source

• The observer speed: v=0• If fs- frequency of the source, λs-

wavelength of the source, v- speed of sound in air

• During an interval of time, the observer detects an additional number of wave fronts = vot/λs ; fo=fs+vot/λs

• fo=fs(v+vo)/v -the frequency heard by the observer ( when moving away: v–vo)

• #2 The sources moving relative to a stationary observer

• Λo=λs-(vs/fs)

• fo=v/λo =v/(λs- vs/fs)=v/(v/fs-vs/fs)

• fo=fs[v/(v-vs)]

• The observer frequency increases when the source moving toward the observer

• When moving away: v+vs

• General case:

• fo=fs[(v+vo)/(v-vs)]

• Interference of a sound waves

• If the path difference r2-r1 is zero or some integer multiple of wavelengths, then constructive interference occurs, and r2-r1 =nλ; (n=o,1,2…)

• When destructive interference occurs:

• r2-r1 =(n+1/2)λ; (n=o,1,2…)

• Standing waves• The superposition principle traveling waves

move in both direction on the string• Standing wave- if the string vibrates at exactly

same frequency• A node- 2 traveling wave have a same

magnitude but opposite directions ( no motion on a string)

• Antinode- midway between 2 adjactent nodes ( the maximum amplitude)

• All points on the sting oscillate together with the same frequency but different points have different amplitudes of motion

• The ends of the string must be nodes, because these points are fixed

• The distance between a node and a antinode = λ/4

• There are two segments, so, L=2(λ/4)=λ/2 and λ=2L

• The frequency of the vibration:• f=v/λ =v/2L• v=√F/μ• f=1/2L√F/μ fundamental frequency or

first harmonic

• Second harmonic or first overtone, when inserting an additional node-antinode segment

• f2=v/λ2=v/L =2 (v/2L)=2f

• Third harmonic (second overtone)

• f3=v/λ3=3v/2L =3f

• Harmonic series:

• fn=nf =n/2L√F/μ= nv/2L , n=1,2,3