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Sound

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**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

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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

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**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 =P/A

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**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)

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**#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)

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**#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)]

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**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…)

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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

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**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

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**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

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