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