Spring 2024

This experiment makes use of the concepts of superposition and interference of waves. You have seen this material in lecture, if you need a refresher we provide a brief summary here.

One member of the group should click on the link below to start your group lab notebook. (You may be asked to log into your UChicago Google account if you are not already logged in.) Make sure to share the document with everyone in the group (click the “Share” button in the top right corner of the screen) so each member has access to the notebook after you leave lab. Choose one member of your group to be the designated record-keeper.

For this part of the lab your apparatus consists of a pair of speakers, a function generator, and a sound pressure level (spl) meter. Set up the audio interference experiment shown in Fig 3. Use an audio frequency of about 5 kHz. (Keep unnecessary reflecting surfaces away.)

Change the position of one of the speakers relative to the other speaker and the sound pressure level (SPL) meter while observing the signal from the SPL meter on the scope. Consider the following which are related to the principle of superposition:

• What causes the response on the sound level meter to reach a maximum? What causes it to reach a minimum?
• What happens if you reverse the connections to one of your speakers? Why?

For the second part of the lab you will measure the frequency of microwaves produced by a PASCO microwave transmitter by measuring the speed of light and then the wavelength of the radiation from the transmitter.

To measure the wavelength of the microwaves you will build a Michelson interferometer. If you are unfamiliar with how a Michelson interferometer works, wikipedia has a nice description.

To construct your interferometer you have both a microwave transmitter and a receiver, two metal reflectors, and a white board which is made of a material that is 50% reflective for microwaves. Arrange these components to build your interferometer. Then by changing the path length of one of the arms of the interferometer while monitoring the intensity of the output, you can find the wavelength.

Now, instead of driving two speakers with an identical source (e.g. creating coherent waves), we will drive two speakers with different sources (e.g. creating incoherent waves).

In this case, the phase difference between the two waves will change continuously. If the two waves are superimposed there will be a periodic variation in the amplitude of the resulting wave which is equal to the difference in frequency of the two waves. This variation in the amplitude of the sum of the two frequencies is called beating. This variation in amplitude for sound waves manifests as a volume which varies periodically with a frequency that is equal to the difference between the two frequencies.

The production of beats is shown in Fig. 4.

Figure 4: Beats formed by the addition of waves with two different frequencies

The phenomena of Beats is often used to make very precise measurements of two frequencies. Various resonance experiments such as pulsed nuclear magnetic resonance which rely on precisely matching the frequencies of two signals are one such example, and this is an experiment you will encounter in the third year advanced lab course as a physics major.

For this part, you will use two function generators, a beat box, and a scope. The “beat box” provided takes the two input signals and sends one signal to the left ear of each headphone and one signal to the right ear of each headphone. In this way, you can hold the headphones up to your ear either individually (to hear one signal at a time) or together (to hear both).

Choose frequencies of about 400 Hz and adjust the loudness to be close to the same for both headphones and at a comfortable listening level. Keep the loudness low enough to avoid distortion in the headphones.

Initially place both left and right phones close to one of your ears. Adjust one of the frequencies until beats are clearly audible.

At the same time, look for the signals on the oscilloscope. You should arrange things so that you can see one sine wave on Channel 1, the other sine wave on Channel 2 and use the difference feature of the scope (in the “Math” menu) to display the beat frequency.

What happens if we put on the headphones and drive the two ears at different frequencies? In this mode, each ear drum is presented with a single frequency and should, therefore, not experience beats.

Without changing the frequencies used earlier, place one phone on each ear and listen for beats. 

• In your notebook, describe carefully what you hear.

Repeat the above exercise using frequencies of about 500 Hz and 1000 Hz.

• Can you hear beats at these higher frequencies? 

Beats are often used as a way to identify an unknown frequency (or to tune a source to a known frequency).

As an example, try using the above beats techniques to identify the frequencies of the strings on the Ukulele's in the lab. This exercise is just for fun. If you are a musician or a singer your ear-brain combination is more likely to recognize the beating phenomena, but give it a try regardless.

You can use the function generator to drive one of the speakers at a known frequency then pluck a string and listen for the beats. Or you might be able to see the beating on the scope by using the SPL meter to record the sound from both the Ukulele and the speaker. Both methods are challenging so this is not a mandatory part of the lab.

For reference the frequencies of an in tune Ukulele are (from left to right when looking at the front of the instrument) approximately 392Hz, 262Hz, 330Hz, and 440Hz. Please do not try to tune the instruments, this will just result in string breakage over time. Simply use the above frequencies as a starting point for determining the actual frequency of the strings.

After the lab, you will need to write up your conclusions. This should be a separate document, and it should be done individually (though you may talk your group members or ask questions).

The conclusion is your interpretation and discussion of your data. What do your data tell you? How do your data match the model (or models) you were comparing against, or to your expectations in general? Your conclusions should always be based on the results of your work in the lab. It is not acceptable to evaluate the results of an experiment by comparison to known values or any other form of preconceived expectation. Your conclusions need to be supported by your data. If your data are inconclusive or in disagreement with regard to your expectations then your conclusion should reflect that.

REMINDER: Your report is due 48 hours after the lab. Submit a single PDF on Canvas.