16.1 Propagation of a Disturbance
16.1 Pulse traveling to the right y (x, t) = ƒ(x – vt)
16.2 Pulse traveling to the left y (x, t) = ƒ(x + vt)
16.2 The Traveling Wave Model
16.3
16.4
16.5
16.6
16.7
16.8 Angular wave number
1ƒ
T=
y(x,t) ≡Asin
2πλ
x−vt( )⎡
⎣⎢
⎤
⎦⎥
y(x,t) ≡Asin 2π x
λ−tT
⎛
⎝⎜⎞
⎠⎟⎡
⎣⎢
⎤
⎦⎥
y(x,0) =Asin
2πλx
⎛
⎝⎜⎞
⎠⎟
v =
∆x∆t
=λT
k ≡
2πλ
16.2 The Traveling Wave Model, cont.
16.9 Angular frequency
16.10 Wave function for a y = A sin (k x – t)
sinusoidal wave
16.11
16.12 Speed of a sinusoidal wave v = λƒ
16.13 General expression for a y = A sin (k x – t + ) sinusoidal wave
22 ƒ
T
π π= =
v =
k
16.2 The Traveling Wave Model, cont.
16.14
16.15
16.16 vy, max = A
16.17 ay, max = 2A
v
y=dydt⎤
⎦⎥x=constant
=∂y∂t
=−Acos kx−t( )
ay=dvydt
⎤
⎦⎥⎥x=constant
=∂vy∂t
=− 2Asin kx−t( )
16.3 The Speed of Waves on Strings
16.18 Speed of a wave on a
stretched string v =
Tμ
16.5 Rate of Energy Transfer by SinusoidalWaves on Strings
16.19 dK = ½ (μdx) vy2
16.20 Eλ = Uλ + Kλ = ½μ2A 2λ
16.21 Power of a wave ℘ =
12
μ 2A2v
16.6 The Linear Wave Equation
16.22
16.23
16.24
F
y∑ ≈T(tanθB −tanθA)
Fy∑ ≈T
∂y∂x
⎛
⎝⎜⎞
⎠⎟B−
∂y∂x
⎛
⎝⎜⎞
⎠⎟A
⎡
⎣⎢⎢
⎤
⎦⎥⎥
F
y∑ =may =µ∆x∂2y∂x2
⎛
⎝⎜⎞
⎠⎟
16.6 The Linear Wave Equation, cont.
16.25
16.26 Linear wave equation for a
string
16.27 Linear wave equation in
general
( ) ( )2
2B A
y x y xy
T t x
μ ∂ ∂ − ∂ ∂∂=
∂ Δ
2 2
2 2
y y
T t x
μ ∂ ∂=
∂ ∂
2 2
2 2 2
1y y
x v t
∂ ∂=
∂ ∂