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Minilab 1 Standing Waves

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.

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Minilab 1 Standing Waves

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

  2. 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 Department of Physics & Astronomy

  3. 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 Page 3 Department of Physics & Astronomy

  4. 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 Page 4 Department of Physics & Astronomy

  5. 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 theory The sum of the two waves (“superposition”) Anti-Nodes Nodes Page 5 Department of Physics & Astronomy

  6. 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: theory l l/2 3l/2 Page 6 Department of Physics & Astronomy

  7. Node on top of the pulley wheel Node somewhere beyond the wave driver equipment Mechanical Wave Driver creates waves (Frequency and Amplitude controlled by Capstone Software) Mass creates tension in string: T = mg Page 7 Department of Physics & Astronomy

  8. Experimental Determination of Speed of Wave • The velocity of the wave can be calculated as follows • V = f l (or ) • (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 Page 8 Department of Physics & Astronomy

  9. Once you have collected your data, you will need to plot f versus 1/λin 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 Page 9 Department of Physics & Astronomy

  10. Theoretical Determination of the Speed of the Wave Important: The string is elastic and gets stretched under tension.  procedure However: It is easier to determine Put the loose string on the scale and measure the mass Measure the full length of the un-stretched string with a ruler Calculate Page 10 Department of Physics & Astronomy

  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: procedure Page 11 Department of Physics & Astronomy

  12. 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: procedure Page 11 Department of Physics & Astronomy

  13. 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 procedure Page 11 Department of Physics & Astronomy

  14. To compare the theoretical and measured velocities, use the % difference calculation: procedure Page 12 Department of Physics & Astronomy

  15. 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! Page 14 Department of Physics & Astronomy

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