Chapter 19 Sound waves 19-1 Properties of Sound waves 19-2 Traveling sound waves 19-3 The speed of sound 19-4 Power and intensity of sound waves 19-5 nterference of sound waves 19-6 Standing longitudinal waves 19-7 Vibrating system and sources of sound 19-8 Beats 19-9 The Doppler effect
Chapter 19 Sound waves 19-1 Properties of Sound waves 19-2 Traveling sound waves 19-4 Power and intensity of sound waves 19-3* The speed of sound 19-5 Interference of sound waves 19-6* Standing longitudinal waves 19-7* Vibrating system and sources of sound 19-8 Beats 19-9 The Doppler effect
19-1 Properites of sound waves When we discuss sound waves, we normally mean longitudinal wave in the frequency range 20 Hz to 20,000 HZ, the normal range of human hearing For simplification we will consider the sound wave in 1D case
When we discuss sound waves, we normally mean longitudinal wave in the frequency range 20 Hz to 20,000 Hz, the normal range of human hearing. For simplification, we will consider the sound wave in 1D case. 19-1 Properites of sound waves
In Fig19-2, as the piston (活塞) moves back and forth, it alternately compresses and expands certain (使稀薄)) the air next to it conditions X This disturbance travels down the tube as a sound AP wave 0 X p(x,t)=po+△p(x,D) △x ipm (x,D)=P0+△P(x,D) It is convenient to use density and pressure to describe the V X properties of fluids Fig 19-2
Fig19-2 In Fig19-2, as the piston (活塞) moves back and forth, it alternately compresses and expands (使稀薄)) the air next to it. This disturbance travels down the tube as a sound wave. x x x x v m u P0 0 m S m pm x (x,t) (x,t) = 0 + P(x,t) P P(x,t) = 0 + It is convenient to use density and pressure to describe the properties of fluids. Under certain conditions
19-2 Traveling sound waves 1)Let us assume that the pistol is driven so that the density and pressure of air in the tube will vary as a sine function △p=△OnSn(kx-Ot) (19-1) △P=△PnSi(kx-ot) (192) 2)What's the relationship between Ap and AP From the definitions of bulk modulus(体模量/膨胀系数) (Eq(15-5)B=A and density p=m, when m is fixed,We have △ν △v △P △ν n=△phn B
1) Let us assume that the pistol is driven so that the density and pressure of air in the tube will vary as a sine function. (19-1) (19-2) 2) What’s the relationship between and ? From the definitions of bulk modulus(体模量/膨胀系数) (Eq(15-5)) and density , when m is fixed, we have sin( k x t) = m − P P sin( kx t) = m − ( ) v v P B = − v m = B ρ P B P ρ v v ρ v v v m v v m ρ 0 2 Δ Δ ) Δ ( Δ Δ = − Δ = − = − = = 19-2 Traveling sound waves P
or△ △P (193) B 3How to find the displacement of an element of gas inside the tube? The undisturbed density of Oxis OX ox A is the corss- iS(x+Sxt) Aδx sectional area SIX 8x=x"x′=[x+x+(x+8,)-x+8x+(x: xx 6x[1+ S(+ar, t-s(x 6x[1+ Sm ASx 1+osar P(1-as/Ox), if as/ax <<1 △p=p-po=-pOs/Ox (196)
3) How to find the displacement of an element of gas inside the tube? B m Pm 0 = (19-3) x=0 x s(x,t) s(x+ ,t x ) x' x x’ x’’ x A x m 0 = The undisturbed density of is x A is the corsssectional area. x ' = x ''-x' = [x + x + s(x + x ,t)]−[x + x + s(x ,t)] ] ( , ) ( , ) δ [1 x s x x t s x t x + − = + (1 ), 1. ' 1 0 0 + = = ρ - s/ x if s/ x s/ x ρ A x δm ρ s x = −0 = −0 / (19-6) or ] s δ [1 x x = +