PHY 2048L
Lab 9

Standing Waves on a String

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Updated: 1/21/2013
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This lab is only loosely based on "Lab 21". The lab manual holds the frequency fixed and varies the wavelength, while we will keep the wavelength fixed and vary the frequency. We can do this because we are using much fancier equipment than they use in the lab manual, equipment that we will use for AC circuit labs next semester.

Note: The lab manual uses "rho" for mass per unit length, whereas we use "mu".
You should change the equations to reflect the ones we use in class.

Guiding Question:

Note: We test this with our result for the experimental value of the wavelength, addressed in a post-lab question. However, your abstract should also mention the precision of your data based on post-lab question 2 as well as the uncertainty in the slope of the fit you did and the linearity of that fit.

Preparing for the lab:

Read the theory for "Lab 21" (pages 217 to 218) in the lab manual before answering the questions on LON-CAPA.

You should also review the procedure handout and pictures below to get a sense of the changes from what is in the lab manual.

We will keep the wavelength constant and vary the frequency as we vary the tension. (This requires a significant change in the data tables, so you will also get a handout with a revised data table for this lab.) Read through the procedure handout and use it to make notes in your lab manual saying what will be done.

You can also ignore the data table and post-lab questions in the lab manual. We will use a modified data table (32 kB pdf), and the handout will give revised post-lab questions that reflect what we actually did (replacing wavelength with frequency, or vice versa). Ask questions before you leave the lab if what you need to do is not clear.

Comment

The lab description in the manual assumes you have a fixed frequency source (at the 60 Hz line frequency) and thus varies the tension to get different numbers of nodes. Because we have a very accurate way of adjusting the frequency, the procedure for this lab will be essentially the reverse of the one described in the manual: We will keep the number of nodes and the wavelength constant, and find the frequency required to produce that standing wave for a range of tensions. See handout for details.

The mass per unit length of the string will be measured at the start of the first lab. It should be about 0.35 g/m or 0.15 g/m depending on which string we use.

We will vary the mass used to put the string under tension and measure the frequency required to produce three antinodes (the n=3 mode) on the string. The slope of the fitted line will then give us an estimate of the wavelength that can be compared to the wavelength determined from a measurement of the length of the string between the driver and the pulley.


Apparatus

pulley, backdrop, driving motor, and wave generator

Blue backdrop makes the string (not shown in this picture) visible. String goes over the pulley at left and is attached to the driving motor (actually a speaker) at right with frequency set by the wave generator (see closeup below).

connections for wave generator (bottom) and frequency counter

Closeup of coax cable connections for wave generator (bottom) and frequency counter plus 'tee' and splitter for feed to speaker. The wave generator controls both the frequency (knob at far right) and amplitude (knob just to the left of the coax) of the wave while the frequency counter gives an accurate reading of the frequency.

Be sure the "sine wave" button is pushed in. This equipment is used for several labs in PHY2049, and the shape of the wave is varied in one of them.

 
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