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

2. 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 & AstronomyPage 2

3. Physics 2225 – Standing Waves THEORY v Department of Physics & AstronomyPage 3

4. 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 & AstronomyPage 4

5. 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 the two waves (“superposition”) Department of Physics & AstronomyPage 5

6. 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: /2  /2 Department of Physics & AstronomyPage 6

7. 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 & AstronomyPage 7

8. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 8  The velocity of the wave can be calculated as follows V = f  or f = v/  (read off frequency in Capstone Software, measure  when you see a standing wave pattern).  Start from low frequency and observe several different standing waves (different f and ).  Plot f versus 1/  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

9. 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 & AstronomyPage 9

10. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 10

11. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 11 You then need to get l unstretched with your ruler by taking the string off the pulley system To find  stretched, we need the following equation: m stretched =  unstretched * l unstretched When we plug this into  stretched, we get Please correct this last equation in your lab manual on page 14! It is incorrectly printed there.

12. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 12

13. 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 & AstronomyPage 14