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 Node on top of the pulley wheel Department of Physics & AstronomyPage 7 Node somewhere beyond the wave driver

8. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 8  The velocity of the wave can be calculated as follows V = f  or  (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 Theoretical Determination of the Speed of the Wave Important: The string is elastic and gets stretched under tension.  However: It is easier to determine 1)Put the loose string on the scale and measure the mass 2)Measure the full length of the un-stretched string with a ruler 3)Calculate

11. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 11 Next, you need to determine how and are related. Imagine two situations: 1) Stretched string (with tension) in our setup (no mass hanging on string): Mass of the part of string between the pulley and the rod: M Length of string between the pulley and the rod:

12. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 11 Take off the mass to release the tension  the string shrinks a bit. 2) Un-stretched string (no tension) in our setup (no mass hanging on string): Mass of the same string portion: M Length of the same string portion:

13. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 11 So, we have two equations relating to these two situations: We can combine these and eliminate M (the mass of that string portion): Then we can get an equation for the speed of the wave of the stretched string

14. Physics 2225 – Standing Waves PROCEDURE Department of Physics & AstronomyPage 12 To compare the theoretical and measured velocities, use the % difference calculation:

15. 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 consist of two or three people. Make sure all members of the group write their name on the lab report! Department of Physics & AstronomyPage 14