physics 2225 – standing waves minilab 1 standing waves page 1department of physics & astronomy
TRANSCRIPT
Physics 2225 – Standing Waves
Minilab 1Standing Waves
Page 1Department of Physics & Astronomy
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
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
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
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
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
Department of Physics & Astronomy
Page 6
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
Department of Physics & Astronomy
Page 7
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
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!
Department of Physics & Astronomy
Page 9
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
Department of Physics & Astronomy
Page 10
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
l
l
m
dunstretche
stretched
dunstretcheltheoretica l
lTv
Physics 2225 – Standing Waves
PROCEDURE
• Finally, to compare the theoretical and measured velocities, use percent difference:
Department of Physics & Astronomy
Page 12
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