PCS 125 - Standing Wave on a String Lab Report 2012

RYERSON UNIVERSITY DEPARTMENT OF PHYSICS LAB REPORT FOR PCS 125 SECTION TITLE OF EXPERIMENT: Standing Wave on a String EXPERIMENTERS: (Full names and ID’s) -19050016573500 AUTHORS OF THIS REPORT: EXPERIMENT PERFORMED ON (DATE): February 15th, 2012 REPORT SUBMITTED ON (DATE): February 22nd, 2012 TA’S NAME: Objective and background: Many vibrations of stretched objects such as the motion of turning fork and a string are producing standing wave. Therefore, when a string fixed at one end is stretched; it will vibrate and create a standing wave. However, standing wave is formed, when two traveling waves travel in the opposite direction, have the same frequency, speed and amplitude are interferes. Also, resonance phenomena occurs when an outside force is applied that have frequency same as the system’s own frequency. The purpose of this lab; however, is to determine experimentally the resonance modes of stretched string and how the speed and tension on the oscillation string relates to its length, mass, resonance frequency and modes of vibration by using weight, string and variable frequency vibrator. In this lab, we have computed the standing wave by adjusted the frequency of the vibrator of about 350 Hz and using mass of 100g to get standing wave of one nodes ( n=1). Then, we have increased the frequency to obtain standing wave of two and three nodes (n=2, n=3) using the same mass of 100g and record the value of frequency. Then, the frequency of standing wave was calculated by using different mass (200g and 300g) and then recording the values of the wavelength. The following equations were used to calculate the data; The wavelength of the standing wave was computed by using this formula; =2L/n The speed of the wave will be calculated with; v=f Where v is the speed of the standing wave f is the frequency in Hz is the wavelength in m This equation shows the relationship between the speed and tension on the stretched string of the wave; v=T/? Where T is the tension on the string ? is the linear density The resonance frequency was computed by using this equation; fn=n/2L T/? fn is the resonance frequency n is the number of nodes L is the distance of the string T is the tension of the string ? is linear density of the string (mass per unit length) In conclusion to all of the equations above, the observation and calculation will prove each equation in their own way. Materials Variable frequency vibrator Wooden bridge Pulley String Generator / Amplifier Balance Scale Meter stick Weigh and weight hanger Vibrator Weight hanger Generator Wooden bridge String Meter stick Pulley Balance Scale Procedure In this lab, we have calculated the frequency, speed and wave length of standing wave by adjusted the variable frequency vibrator and using different mass values. The apparatus was set up on the table by putting the vibrator at the table and pulley was attached at the other side and a string was attached to the vibrator and run over the pulley. Then, the wooden bridge was slide under the string to adjust the portion of the string that can be resonance by vibrator. The length was measured between 1 and 1.5 meter using meter stick. Then the tension was set up by hanging a mass of 100g. The frequency of the vibrator was adjusted to get standing wave of n=1 and the value of the frequency were recorded. The frequency was increased in order to obtain a standing wave of 2 and 3 loops. The step was repeated to maximum frequency of about 350 Hz. The wavelength of each standing wave pattern was computed by using this formula =2L/n. The steps above were repeated by using mass of 200g and 300g. The tension in the string was computed by multiplying the mass by 9.8m/s2. References: http://www.physics.ryerson.ca/sites/default/files/u11/exp/exppcs125/Stading%20Waves.pdf http://www.physics.ryerson.ca/labs/PCS125