Standing Waves

Kieff, Ptj, Wikipedia, public domain

St. Mary's Physics Online

B) Standing Wave – waves produced when two waves of the same frequency and amplitude travel in opposite directions in the same medium (Musical instruments)

Remember the old slinky song? - slinky.wav

Standing Wave
David M. Harrison

How many antinodes are in each picture?

(focus on the lower half of the guitar)

Physics of the Acoustic Guitar
Fletcher

2, 4, 10

Click on the frequencies above

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 Maximum Destructive Interference Occurs at the Nodes

Standing waves can also be produced by reflection

How many nodes?

5

How many antinodes?

4

How many waves?

2

C. K. Eng

How many wavelengths?

Wikipedia, Houtlijm, public domain

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 One Antinode Four Antinodes

Illustration of vibrations of a drum - Oleg Alexandrov
Public Domain Image

 How many antinodes? How many wavelengths?

2 antinodes, wavelength = 3.0 m

AP Physics

L = distance between walls

String fixed at both ends
or Open Pipe Both ends

L = (nl/2)

n = 1,2,3 ....

since v=fl

then

fn = n[v/2L]

n = 1,2,3 ....

Each frequency is a multiple of the fundamental frequency

Pipe Open at One End

Closed at one end

L= [n/4]l

n = 1,3,5,7 .....

since v=fl

then

fn = nv/4L

n = 1,3,5,7 .....

frequency goes up by 2 times fundamental and are divisible by ODD number

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 indentical frequency sources

Enrichment

Enrichment

Berkeley Univ.

Water Drop in Zero g