Standing Waves on a String Laboratory, Lab Reports of Physics

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Standing Waves

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Physics 1051 Laboratory #2 Standing Waves

Prelab

Write experiment title, your name and student number at top of the page. Prelab 1: Write the objective of this experiment. Prelab 2: Write the relevant theory of this experiment. Prelab 3: List the apparatus and sketch the setup. Have these ready to be checked by lab staff at the door on the day of your lab. LR LR LR

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Standing waves

Waves on strings are transverse waves. When a string is vibrating at its fundamental frequency, the wave pattern looks like the one shown below.

Standing waves are created by an interference pattern of waves whereby there are fixed points of constructive and destructive interactions. At points where there is constructive interference, there is a relative maximum amplitude which is referred to as an antinode. Above, this would be in the middle of the image. Where destructive interference occurs, amplitude is a minimum and a node is created. In the case above, the nodes would be the ends.

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Wave speed on a string

The wave speed! can be determined using the frequency " and the wavelength # by the expression

The wave speed on a string is also given by

where & is the tension in the string and μ is the linear mass density.

The mass density ( is calculated by the mass per unit length of the string, namely

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Experimental Setup

The string vibrator will generate waves at a fixed frequency. These incident waves travel the length of the string to the pulley at the end of the bench where the waves will be reflected back towards the vibrator. At certain distances between the vibrator and the pulley, the incident and reflected waves will begin to interfere and create a standing wave pattern. This standing wave pattern is an example of resonance , where an external force or boundary condition can produce an increase in amplitude at specific frequencies.

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Wavelength Prediction

In order to produce a standing wave pattern, the distance from the string vibrator to the pulley needs to be a multiple of half a wavelength.

We’ll use the wavelength to guide the placement of the string vibrator to create a standing wave pattern. Using the wavelength, and the understanding that the vibrator must be placed near a node, we should be able to easily produce a good standing wave pattern.

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Wavelength Prediction

The linear densities of the strings ( 34567 = 1.42×10 =>^ ?@/) ( (^) AB44CD = 1.50×10 =F^ ?@/) G( (

Lab Report 1: Indicate your string vibrator frequency and string colour in your lab workbook. We take the uncertainty in frequency to be zero, G" = 0.

Lab Report 2: Write the linear density of your string in the form ( ± G(.

Lab Report 3: Choose a mass to provide the tension in the string, based on information on previous slide, and record this mass. Calculate the tension. Include uncertainty.

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Wavelength Prediction

Lab Report 4: Using " and (, and your chosen tension, determine the wavelength of your wave with uncertainty. Write in the form

± G#.

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We can use this wavelength value to construct our experimental setup. In the example to the right, the setup has a total of 2.5 wavelengths from the vibrator to pulley.

Use this information and the following slide to set up your apparatus similarly. As the nodes at the vibrator and pulley are difficult to measure, the setup

! works best by keeping the total length at least 1.5 wavelengths.

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Equipment Warning.

The string vibrators should only be plugged in while

collecting data, and should not be running continuously.

The devices get HOT and as they do, the frequency may

shift and disrupt your data collection, or can cause burns.

DO NOT leave string vibrator running for more than a few

minutes.

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Wavelength Measurement

Use your chosen mass in which you calculated tension and create a standing wave pattern.

Measure the wavelength by using the orange triangle to mark the positions of the nodes IJ and IK, as shown above, on the paper. Using a meter stick, we can measure ΔI and, knowing the number of wavelengths between IJ and IK, we can measure #.

CP Have an instructor check your setup and initial your lab report.

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Summary & Conclusion

Lab Report 8 : Briefly summarize your experiment, in a paragraph or two, and include any experimental results.

Lab Report 9: List any sources of experimental uncertainty and classify them as random or systematic.

Include your prelab and all data analysis with your report.

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