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Physics 2225 – Standing Waves Minilab 1 Standing Waves Page 1 Department of Physics & Astronomy

Minilab 1 Standing Waves

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Minilab 1 Standing Waves. Page 1. PURPOSE. Today, we will observe standing waves on a string in order to learn and verify how the formation of standing waves depend on: Excitation Frequency Tension of the string Linear mass density of the string. Page 2. THEORY. - PowerPoint PPT Presentation

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Page 1: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

Minilab 1Standing Waves

Page 1Department of Physics & Astronomy

Page 2: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

PURPOSE

Today, we will observe standing waves on a string in order to learn and verify how the formation of standing waves depend on:

• Excitation Frequency• Tension of the string• Linear mass density of the string

Department of Physics & Astronomy Page 2

Page 3: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

THEORY

When a wave moves along a string, we say the wave is propagating along the string, as shown.

• The linear mass density is related using:

• The density and the tension of the string (T) affect the velocity that it propagates at:

v

Department of Physics & Astronomy Page 3

Page 4: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

THEORY

Note that waves reflections depend on how the string is attached at one end.

• End of string is fixed, the wave gets inverted

• End of string is loose, the wave is not inverted

Department of Physics & Astronomy Page 4

Page 5: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

THEORY

We use the term superimposed to mean two waves that are overlapping. Below, these two waves are travelling in opposite directions.

Nodes Anti-Nodes

Moving to right

Moving to left

The sum of thetwo waves (“superposition”)

Department of Physics & Astronomy Page 5

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Physics 2225 – Standing Waves

THEORY

If the length remains unchanged, standing waves only occur at specific frequencies.

• In our case, we have strings with nodes at both ends, which produces the following:

l/2 3l/2l

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Physics 2225 – Standing Waves

EQUIPMENT

Mechanical Wave Driver creates waves(Frequency and Amplitude controlled by Capstone Software)Mass creates tension

in string: T = mg

The two nodes are here

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Physics 2225 – Standing Waves

PROCEDUREDepartment of Physics & Astronomy Page 8

The velocity of the wave can be calculated as follows

V = f l (or f = v/ l)

(read off frequency in Capstone Software, measure l when you see a standing wave pattern).

Start from low frequency and observe several different standing waves (different f and l).

Plot f versus 1/ l The slope of this graph equals v.

Repeat the procedure using a different tension in the string (use a different mass at the end of the string). V should be different because it depends on the tension T.

EXPERIMENTAL DETERMINATION OF SPEED OF WAVE

Page 9: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

PROCEDURE

• Once you have collected your data, you will need to plot f versus 1/λ in Excel. The slope of your graph is equal to v.

If you are still having struggles with plotting in Excel, please refer to the Excel Tutorial online, or make sure your lab partner can explain it to you!

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Page 10: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

PROCEDURE

Theoretical Determination of the Speed of a Wave

• As we saw above, the theoretical speed is:

• To find , you will first need to find with a ruler and the scale. Also note that 2 m

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Physics 2225 – Standing Waves

PROCEDUREDepartment of Physics & Astronomy Page 11

• You then need to get lunstretched with your ruler by taking the string off the pulley system

• To find mstretched, we need the following equation:

mstretched = munstretched * lunstretched

• When we plug this into mstretched , we get

• Please correct this last equation in your lab manual on page 14! It is incorrectly printed there.

stretched

dunstretchedunstretche

stretched

stretchedstretched l

llm

mm

dunstretche

stretched

dunstretcheltheoretica l

lTv m

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Physics 2225 – Standing Waves

PROCEDURE

• Finally, to compare the theoretical and measured velocities, use percent difference:

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Page 13: Minilab 1 Standing Waves

Physics 2225 – Standing Waves

FINAL HINTS

Homework Policies• You must do your homework BEFORE

CLASS, and everyone must turn in their own work.

Lab Report Policies• Submit one lab report per group. Groups

should generally consist of two people.• Make sure both members of the group

write their name on the lab report!

Department of Physics & Astronomy Page 14