Q1 - Standing Waves

• • Tension wave • • Wave on a string transverse Sound wave • • • Longitudinal Air inside a tube Density of air above or below equilibrium point General Physics 2 Induction 1

•

Waves on a Slinky

Measure the wavelength and period for the first, second, and third harmonics using meter sticks and stop watches. To measure the frequency, wiggle the slinky ten times and measure the time. Ten divided by the time is the frequency.

• Create a formula for frequency of any of the harmonics on the slinky in terms of the first harmonic.

General Physics 2 Induction 2

 •

Standing Wave

Wave travelling to the right   

A

sin 

kx

 

t

 • Reflected wave travelling to the left   

A

sin 

kx

 

t

   • The total wave function (superposition principle)   

A

sin 

kx

 

t

 

A

sin 

kx

 

t

 • Simplifies to the equation for a standing wave    2

A

sin

kx

cos 

t

General Physics 2 Induction 5 



String fixed at both ends

•  2

A

sin

kx

cos 

t

Nodes occur when kx = 0 = kL

kL



n



k L

  2 

n

  2 

n



L f

General Physics 2 

v n

2

L

Fundamental frequency when n = 1 Induction 6 

Sources of sound

• • • • String instruments Strings are fixed at both ends.

sound is amplified by • • sounding box sounding board

Figure out the equation for harmonic wavelengths in terms of L, where L is the length of the unstretched string

.

General Physics 2 Waves & Sound 7

Pair Problem

• A highway overpass was observed to resonate as one full loop when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good? General Physics 2 Waves & Sound 8

Interactive Physics

• Exploration of Physics • • • Waves on a Rope Adding Waves Standing Waves General Physics 2 Waves & Sound 11