Physics 204 - Experiment 2 - Standing Waves
Introduction
Standing Waves
Goals
The goal of this lab is to investigate how various physical properties of a string affect its behavior while undergoing oscillatory motion.
Equipment check
Please make sure your station has all of the following items. If not, check again, then talk to your lab instructor.
- Slotted Mass set
- 12" ruler
- Meter stick
- track
- Wave Oscillator Unit
- Sine wave generator
- Thick white string
- pan
Warm Up Exercise
Here are a warm up questions to get familiar with standing waves on a string.
To Do: One person holds the white stretchy string so that it is just barely taught. Another lab partner plucks the string.
What type of wave is created?
What mode of oscillation results?
If the tension in the string is 10 N, and its linear mass density is 4.3 g/m, what will the frequency of the n = 1 mode be, assuming the string is about 1 meter?
What will happen to the linear mass density if the person holding the string stretches it? Will $\mu$ increase, decrease, or stay the same?
Stretch the string and listen to the frequency of the string as you do so. What do you observe (or hear) happening to the frequency
A little simulation
Here is a sim showing the components of standing wave. Adjust the slider to see the effects on the standing wave.
Experiment 1
Verify the relation between number of antinodes and the wavelength of the standing wave: $$\frac{2L}{n} = \lambda$$ To do this, you'll need to take several measurements in which you change only the frequency of oscillation, and the build a table of data that has the number of antinodes visible ($n$) and the measured length of the wave. For example, the fundamental harmonic, $n = 1$, has a wavelength of $2L$. In your lab notebook, make a table of data like this:
| n | $\lambda$ | $f$ |
|---|---|---|
| 1 | ||
| 2 | ||
| $\vdots$ | ||
| 5 |
The basic setup of a vibrating string.
- Set up the string as shown in the figure.
- Place 2x100 gram weights on the slotted mass hanger.
- Adjust the frequency knobs until you see the fundamental resonance. Record the wavelength and the frequency.
- Repeat for up to $n=5$.
After you have this data, make a plot in excel showing the relation between $1/n$ (vertical axis) and $\lambda$ (horizontal axis). Since the relation between these parameters is: $$ \frac{1}{n} = \frac{1}{2L}\lambda$$ The slope of the resulting graph should given by $\frac{1}{2L}$. Confirm that this is the case.