General Physics 2 Induction 1

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

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

General Physics 2 Induction 5

Standing Wave• Wave travelling to the right

• Reflected wave travelling to the left

• The total wave function (superposition principle)

• Simplifies to the equation for a standing wave

€

f x, t( ) = Asin kx −ωt( )

€

f x, t( ) = Asin kx +ωt( )

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f x, t( ) = Asin kx +ωt( ) + Asin kx −ωt( )

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f x, t( ) = 2Asinkx cosωt

String fixed at both ends

• Nodes occur when kx = 0 = kL

General Physics 2 Induction 6

€

f x, t( ) = 2Asinkx cosωt

€

kL = nπ

k =2π

λ= nπ

L

L = nλ

2

f = nv

2LFundamental frequency when n = 1

General Physics 2 Waves & Sound 7

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 8

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 11

Interactive Physics

• Exploration of Physics• Waves on a Rope• Adding Waves• Standing Waves