this week – ch. 14 – waves next week – ch. 8 – gravity...
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This week – Ch. 14 – WavesNext week – Ch. 8 – GravityHomework due 11/26, 5 pm (both chapters)
No labs or quiz next week
Quiz this week – Oscillations[Natural frequency, relation between amplitude, velocity, acceleration, energy]
Resonance
md2xdt2
=F0cosDt−kx
x=xdxh
md2xddt2
kxd=F0cosD t Driven
md2xhdt2
kxh=0 Homogeneous
xd=AdcosDt Driven
xh=Acos0 t
Waves – Physical changes that move through space and change in time
LongitudinalConducting medium moves along wave direction.
Sound, p-waves
TransverseMedium moves perpindicular to wave direction
Water waves, light, radio, s-waves
Wave Properties
Wavelength Wave number
FrequencyAngular Frequency
Period
Speed
m
k=2m−1
f Hz cycles /sec s−1 rad /sec
http://phet.colorado.edu/simulations/sims.php?sim=Wave_on_a_String
T=1f=2
s
v=f =
km /s
Wave Speeds
Depend on medium “Stiffer” media havefaster waves. More massive media have slower waves.
vSOUND= P
=330m /s air ,STP
vSOUND=1500m /s water
vSOUND=5000m /s granite
vLIGHT=c=3×108m /s vacuum
vROPE=F m /s
The four strings of a musical instrument are all made of the same material and are under the same tension, but have different thicknesses. Waves travel
A. fastest on the thickest string
B. fastest on the thinnest string
C. at the same speed on all strings
D. not enough information given to decide
If you double the wavelength λ of a wave on a string, what happens to the wave speed v and the wave frequency f?
A. v is doubled and f is doubled
B. v is doubled and f is unchanged
C. v is unchanged and f is halved
D. v is unchanged and f is doubled
E. v is halved and f is unchanged
Formulae for sinusoidal waves
y=Acosk x− t
y=Acos2x−2Tt
A wave on a string is moving to the right. This graph of y(x, t) versus coordinate x for a specific time t shows the shape of the wave at that time.
What are the velocity and acceleration of a particle at point P on the string?
A. velocity is upward and acceleration is zero
B. velocity is downward and acceleration is zero
C. velocity is zero and acceleration is upward
D. velocity is zero and acceleration is downward
E. none of the above
A wave on a string is moving to the right. This graph of y(x, t) versus coordinate x for a specific time t shows the shape of the wave at that time.
What are the velocity and acceleration of a particle at point Q on the string?
A. velocity is upward and acceleration is zero
B. velocity is downward and acceleration is zero
C. velocity is zero and acceleration is upward
D. velocity is zero and acceleration is downward
E. none of the above