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Material Type: Notes; Professor: Losert; Class: PRINCIPLES PHYSICS; Subject: Physics; University: University of Maryland; Term: Unknown 1989;
Typology: Study notes
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TODAY: Ch 16, Waves
HW due Mon
Speed of pulse v -> pulse travels distance vt in time t The shape of the pulse does not change with time
y
x0 x
6 ( , ) 3
y x t x x
= − +
x0 +vt
vt
Initial Shape of pulse:
Speed of pulse/wave propagation in string
T: String tension μ: Linear mass density
Are Units correct?
elastic property inertial property
v =
Reflection of pulse: Fixed End
When the pulse reaches the support, the pulse moves back
Reflection of the pulse
The pulse is inverted
Reflection off Free End
Free end oscillation takes place at endpoint
The pulse is reflected
The pulse is not inverted
Part of the pulse is reflected and part is transmitted
The reflected part is inverted
Wave motion in one period T: vT = λ or v = λ / T
Plug into wave function
We can define the angular wave number (or just wave number), k
The angular frequency can also be introduced again
->
( , ) sin 2 x t y x t A T
π λ
⎡ (^) ⎛ ⎞⎤ = (^) ⎢ ⎜ − ⎟⎥ ⎣ ⎝ ⎠⎦
k π λ
2 T
π ω =
How to create sinusoidal waves on a String
Speed of a fixed point xo :
v (^) y = - ω A cos( kx – ω t )
NOT the propagation speed of the wave!
Other example: Jammed wave in traffic jam moves backward. Individual point (car) in traffic jam moves forward
= 0
y x x
dy v dt
ay = - ω^2 A sin( kx – ω t )
constant
y y x
dv a dt (^) =
