Melde's Vibrating String, 3B22.10

Topic and Concept:

• Wave Motion, [:WaveMotion#StandingWaves: 3B22. Standing Waves]

Location:

• Cabinet: [:WavesSoundCabinet: Waves and Sound] (WS)

• Bay: (A4)

• Shelf: #1

attachment:MeldesString01-400.jpg

Description:

The Pasco driver controlled by a function generator vibrates an elastic cord. By varying the driving frequency and amplitude, one can produce standing waves. The nodes and the antinodes can be seen better by using strobe lights.

Important Setup Notes:

• N/A

Setup and Demonstration:

1. Take the small ring stand with the elastic cord wrapped around it. Unwrap enough cord to stretch the cord across the lecture bench.
2. With the Pasco vibrator, take the looped end of the cord, string in through the forked tip, and attach to the base set screw that is typically used to hold rods. This will anchor the cord.
3. Place a lead brick in front of the vibrator to prevent the cord from pulling or tipping the the vibrator.
4. Place the strobe at each end of the cord in such a way that the strobe light are aimed at the cord and NOT at the students.
5. Set the function generator so that the cord vibrates at it's fundamental frequency.
6. Vary the driving frequency and amplitude to show the other modes of a standing wave fixed at both ends. Be sure to point out the nodes and the antinodes.
7. Use the strobe lights to make the vibrating cord stand still or make it roll in slow motion. The strobe speed can be adjusted on the back of the lamp.

Cautions, Warnings, or Safety Concerns:

• Strobe lights can bother students with epilepsy. This warning should be stated in class before doing the demonstration.

Demonstration:

The fundamental frequency of a wave on a string depends on the speed of wave propagation and the length of the string. The speed of propagation on the string depends on the string tension and the linear mass density as follows

v = Sqrt[T / ρ].

The boundary conditions determine our wavelength. For a string with fixed ends, the wavelength must be an integer multiple of half the length of the string

λ_n = 2*L/n.

Since wavelength and frequency of oscillations of a wave are related to the wave speed by

λ*f = v

we can find that the fundamental (lowest order) frequency is given by

f₁ = v/λ₁ = Sqrt(T/ ρ) / (2*L)

since it's difficult to attain the same the tension and length of the cord, the fundamental frequency will differ every time this demonstration is set up.

Higher order frequencies can be achieved by increasing the frequency of oscillations (done using the function generator) having the form

f_n = v/λ_n = n * Sqrt(T/ ρ) / (2*L)

Videos:

• [https://www.youtube.com/user/LectureDemostrations/videos?view=1 Lecture Demonstration's Youtube Channel]

References:

• [https://en.wikipedia.org/wiki/Melde%27s_experiment Wikipedia - Melde's Experiment]

• [https://en.wikipedia.org/wiki/Standing_wave Wikipedia - Standing Wave]

• [http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html Hyperphysics - Waves on a String]

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