Standing Waves
Partners: Me, Myself, and I
Date: 4/27- 5/14
Date: 4/27- 5/14
Purpose
The purpose of the experiment is to see how the speed of the wave is affected by stretching force and frequency.
Theory
A standing wave is a repeated interference of two waves going in opposite directions. It consists of nodes and antinodes. A node is the point of no displacement and an antinode is the points of maximum displacement. The fundamental is a wave produced from the lowest frequency it takes to make a wave. It consists of two nodes and one antinode. It is also called the first harmonic.
Below is one of the equations used to find the velocity of the standing waves. The lambda stands for the wavelength and the fancy f is the frequency. The standard frequency of power outlets in the United States is 60 Hz.
Below is one of the equations used to find the velocity of the standing waves. The lambda stands for the wavelength and the fancy f is the frequency. The standard frequency of power outlets in the United States is 60 Hz.
Below is and expanded version of lambda where the fancy l is the length of the String, the 2 is the number of waves it takes to complete one wavelength, and the n is the total number of waves.
Below is one of the derived equations for velocity. Lambda has been replaced with the above equation and the fancy f is still frequency.
Below is the second equation used to find velocity. The F is the Force due to Tension and mu is mass per unit length.
Below is the equation for Force due to Tension where mass is multiplied by gravity. The mass is the mass that is on the Mass Hanger plus the Mass Hanger itself.
Below is the equation for mu where mu equals mass times unit length. The mass is the mass of the String and the length is the distance from the Pulley to the String Vibrator.
Below is the other derived equation for velocity. F has been replaced with mhg, where m is the mass of that is on the Mass Hanger plus the Mass Hanger, and mu has been replaced with ms/l, where the mass is the mass of the String.
Experimental Technique
Apparatus
-String Vibrator -Power Supply -String -Clamps -Pulley -Mounting Rod for Pulley -Block of Wood -Masses -Mass Hanger -Scale -Tape Measure -Sharpie Marker -Scissors -Computer -MicroSoft Excel -Table |
Procedure
1. Set up the apparatus. 2. Cut the String longer than the table. 3. Tie the String in a double fisherman's knot to the String Vibrator. 4. Tie a hitch onto the Mass Hanger and place it on the Pulley. 5. Measure the distance from the String Vibrator to the Pulley. 6. Turn on the String Vibrator. 7. Add Masses to the String until you get 10 different standing waves while also getting the uncertainty and marking the String for each wave. 8. Try for the Fundamental and fail while also putting a hole in Mr. Bowman's floor. 9. Record each Mass with the Mass Hanger. 10. Turn off the String Vibrator. 11. Cut the String at each mark and mass it. 12. Calculate the velocity using the two equations. 13. Calculate percent difference. 14. Put all Data into MicroSoft Excel. |
Data
Analysis
Conclusion
In conclusion, the lab went very well. The sources of error were the hanging masses and the pulley. The pulley would not turn easily so it affected how the masses pulled on the string and since the masses were affected by the pulley the uncertainty and Force were slightly off.
Reference
Fundamental Frequency and Harmonics. (n.d.). Retrieved May 14, 2015, from http://www.physicsclassroom.com/class/sound/Lesson-4/Fundamental-Frequency-and-Harmonics
Nodes and Anti-nodes. (n.d.). Retrieved May 14, 2015, from http://www.physicsclassroom.com/class/waves/Lesson-4/Nodes-and-Anti-nodes
Standing Wave Formation on a String. (n.d.). Retrieved May 14, 2015, from http://www.physicsclassroom.com/mmedia/waves/swf.cfm
Nodes and Anti-nodes. (n.d.). Retrieved May 14, 2015, from http://www.physicsclassroom.com/class/waves/Lesson-4/Nodes-and-Anti-nodes
Standing Wave Formation on a String. (n.d.). Retrieved May 14, 2015, from http://www.physicsclassroom.com/mmedia/waves/swf.cfm