812.3 Energy transport via mechanical waves The velocity of wave on a string The wave is viewed from a reference frame moving with the wave so it is seen to be at rest. The disturbance is motionless but the string is observed to move to the left at a constant speed △m(v2/r)=2Tsin(61/2)≈T6 △m=MM,b=M/r (v2/r)=T v=√T/ C s 12. 3 Energy transport via mechanical waves Generalize to the other waves The general relationship for the speed of mechanical waves in material media magnitude of a force factor v OC mass factor Sound wave in solid: vsolid module P Sound wave in lianid Www/B1212 §12.3 Energy transport via mechanical waves 1. The velocity of wave on a string µ µ µ θ θ θ / ( / ) , / ( / ) 2 sin( / 2) 2 2 v T r l l v r T m l l r m v r T T = ∆ ∴ ∆ = ∆ = ∆ = ∆ Q∆ = ≈ The wave is viewed from a reference frame moving with the wave so it is seen to be at rest. The disturbance is motionless but the string is observed to move to the left at a constant speed v. x y T r T′ r θ θ / 2 ∆l r C θ / 2 §12.3 Energy transport via mechanical waves The general relationship for the speed of mechanical waves in material media: 1/ 2 mass factor magnitude of a force factor ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ v ∝ 1/ 2 solid ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ρ E v 1/ 2 liquid ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ρ B v Sound wave in solid: Sound wave in liquid: young´s modulus bulk modulus Generalize to the other waves: