v - Department of Physics & Astronomy at the University of Utah
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Physics 2225 – Standing Waves Minilab 1 Standing Waves Department of Physics & Astronomy Page 1 Physics 2225 – Standing Waves 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 PURPOSE Department of Physics & Astronomy Page 2 Physics 2225 – Standing Waves 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: ๐ ๐= ๐ • The density and the tension of the string (T) affect the velocity that it propagates at: ๐= ๐ป = ๐ ๐ป ๐ ๐ v THEORY Department of Physics & Astronomy Page 3 Physics 2225 – Standing Waves 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 THEORY Department of Physics & Astronomy Page 4 Physics 2225 – Standing Waves We use the term superimposed to mean two waves that are overlapping. Below, these two waves are travelling in opposite directions. Moving to right Moving to left The sum of the two waves (“superposition”) THEORY Nodes Department of Physics & Astronomy Anti-Nodes Page 5 Physics 2225 – Standing Waves 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 l 3l/2 THEORY Department of Physics & Astronomy Page 6 Physics 2225 – Standing Waves The two nodes are here Mass creates tension in string: T = mg Department of Physics & Astronomy Mechanical Wave Driver creates waves (Frequency and Amplitude controlled by Capstone Software) EQUIPMENT Page 7 Physics 2225 – Standing Waves EXPERIMENTAL DETERMINATION OF SPEED OF WAVE ๏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. PROCEDURE Department of Physics & Astronomy Page 8 Physics 2225 – Standing Waves • 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! PROCEDURE Department of Physics & Astronomy Page 9 Physics 2225 – Standing Waves Theoretical Determination of the Speed of a Wave • As we saw above, the theoretical speed is: ๐ฃ= ๐ ๐๐ ๐ก๐๐๐ก๐โ๐๐ • To find ๐๐ ๐ก๐๐๐ก๐โ๐๐ , you will first need to find ๐๐ข๐๐ ๐ก๐๐๐ก๐โ๐๐ with a ruler and the scale. Also note that ๐๐ ๐ก๐๐๐ก๐โ๐๐ = 2 m PROCEDURE Department of Physics & Astronomy Page 10 Physics 2225 – Standing Waves • 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 m stretched ๏ฝ mstretched munstretched ๏ lunstretched ๏ฝ lstretched lstretched ๏ฎ vtheoretical ๏ฝ T munstretched ๏ lstretched lunstretched • Please correct this last equation in your lab manual on page 14! It is incorrectly printed there. PROCEDURE Department of Physics & Astronomy Page 11 Physics 2225 – Standing Waves • Finally, to compare the theoretical and measured velocities, use percent difference: ๐ฃ๐๐๐๐ ๐ข๐๐๐ − ๐ฃ๐กโ๐๐๐๐๐ก๐๐๐๐ % ๐๐๐๐๐๐๐๐๐๐ = ๐ฃ๐กโ๐๐๐๐๐ก๐๐๐๐ PROCEDURE Department of Physics & Astronomy Page 12 Physics 2225 – Standing Waves 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! FINAL HINTS Department of Physics & Astronomy Page 14
