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Standing Waves Handout

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AP Physics

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Standing Waves

 – waves produced when two waves with the same frequency and wavelength travel in opposite directions in the same medium (Musical instruments)

I. Standing Waves - Both Ends Closed

A. Nodes and Antinodes, etc

Ex)

a) Mark the nodes with a dot.

How many are there?

5

b) Mark the ANTInodes with a large X

How many are there?

4

c) How many wavelengths do you see above?

2

d) Maximum CONstructive interference occurs at the

Antinode

e) Maximum CONstructive interference occurs at the

Nodes

B. 1st , 2nd , 3rd ….. Harmonic

Closed End Standing waves always have a node at each end****

1. Fundamental or First Harmonic (N.A.N.)

Draw the first harmonic.

How many wavelengths?

Juan Aguirregabiria and lookang

(Standing Wave length) L = 1/2 wavelength

So l = 2L (Twice the length of the whole standing wave)

2. Second Harmonic (N. A. N. A. N.)

Draw the second harmonic.

How many wavelengths?

L = 4/4 or 1 wavelength

3. Third Harmonic (N. A. N. A. N. A. N.)

Draw the third harmonic.

How many wavelengths?

L = 6/4 or 3/2 wavelengths

So l = 2/3L (or 2/3 the length of the standing wave)

4. 4th Harmonic (N. A. N. A. N. A. N. A. N.)

Draw the fourth harmonic.

How many wavelengths?

L = 8/4 or 2l  

so l = L/2 (or 1/2 the length of the standing wave)

5. 5th Harmonic (N.A.N.A.N.A.N.A.N.A.N.)

Draw the fifth harmonic.

How many wavelengths?

L = 10/4 or 5/2 wavelengths

so l = (2/5)L (or 2/5 the length of the standing wave)

Review - Standing Wave - Both Ends

	L = 1/2 l	Fundamental f
	L = 1 l	2x Fundamental
	L = 3/2 l	3x Fundamental
	L = 2 l	4x Fundamental
	L = 5/2 l	5x Fundamental
	L = 3 l	6x Fundamental
	L =7/2 l	7x Fundamental

3 antinodes 4 nodes

a) Nodes: Max Destructive Interference b) Antinodes: Max. Constructive Interference

L = distance between walls

String closed at both ends
 or Open Pipe Both ends

L = (nl/2)

n = 1,2,3 ....

since v = fl

then

f_n = n[v/2L]

n = 1,2,3 ....

Each frequency is a multiple of the fundamental frequency

D. Open at Both Ends

1/2, 2/2, 3/2, 4/2

L = n(1/2)λ

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showmethphysics.com

Giancoli p. 348) 34, 36

34) Closed

88 Hz is fundamental

36) Open Pipe Fundamental 40 Hz, both are even number multiples of 40 not odd multiple of 20

f = v/2L = 40 Hz = (340 m/s)/2L   L = 4.3 m

Review Book p. 302) 10.

Open at one end

n = 1 fundamental

f = v/4L

= 340 m/s/(4 x .17)

= 500 Hz

p. 303) 10

Beats - Rhythmic interference between two semi identical frequency sources

Beat Frequency = |f₁ - f₂|

Standing Wave II

Enrichment

Standing Waves/Sound/Chladni
Berkeley Univ.

Standing Waves - Wake Forest .U.

(Chladni Disk)

Water Drop in Zero g

School blocks YouTube?
Download the file below.

Large_Free_Sphere_of_Water.mov

Standing Waves
HyperPhysics (offsite)

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