Interference (PHYS143)

Spring 2024

Theory


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.

Experimental procedure


Lab notebook template

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.

The record-keeper role will rotate each week so that everyone gets a chance at it. If a group has three students and does six weeks of lab, then each group member is expected to be record-keeper twice during the quarter.

Interference of coherent sound waves

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?

Use the apparatus to measure the wavelength of the sound waves from the speakers by searching for the interference maxima.

Measure the frequency of the sin wave used drive the speakers on the scope.

Use the measured frequency and wavelength to calculate the speed of sound. Compare with the result you got in last weeks experiment.

Microwave interference using a Michelson interferometer

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.

Use your interferometer to measure the wavelength of the microwave radiation from the transmitter. Using the manufacturer specified frequency for the transmitter (which is printed on the transmitter) calculate the speed of light to confirm that your measurement makes sense.

Keep in mind that it is the TOTAL path length difference that matters for interference. There is a factor of 2 which is easily overlooked the first time you work with interferometers.

Beats

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.

Set both function generators at about 400Hz with a difference between the two of about 1Hz. Once you have set the two frequencies, measure the frequency of each function generator output on the scope as accurately as you can.

Then use the sum or difference feature in the MATH mode of the scope to superimpose the two signals. Measure the resulting beat frequency and compare the two measurements.

Driving one ear

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.

Note that you may need to use the 20db attenuation on the function generator in order to get the sound at a comfortable level.

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.

With both phones at one ear, the mechanism for hearing beats is easily understood: while the two waves are in phase, the air pressure driving the ear drum is larger and the sound is perceived as louder. While out of phase, the pressure is less and is perceived as quieter.

Driving two ears

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? 

The physiology involved here may be summarized as follows: Each eardrum is forced to vibrate by the small pressure changes caused by the vibration of its headphone. The eardrum is mechanically coupled through small bones to another membrane at the entrance to the cochlea, a fluid-filled spiral tube. Inside the cochlea is a membrane containing hair cells which are set in motion by the vibration of the fluid. The hair cells closest to the cochlear entrance are sensitive to high frequencies, while those farther from the entrance are sensitive to lower frequencies. The hair cells convert the mechanical vibrations to electrical signals. The signals from the left and right ears are mixed in each of two sets of neurons in the brain stem. One set of neurons is sensitive to high frequencies (typically kHz.) and detects intensity. At high frequencies, the sound shadow cast by the head gives rise to differences in intensity from left to right and is used to judge direction of the sound source. The other set of neurons, sensitive to lower frequencies (typically 200 Hz.), detects phase or time differences to judge the direction of the sound source. The detection of beats with different frequencies sent to the left and right ears depends on the functioning of the lower frequency, phase-sensing neurons.

It has been observed that some people can hear beats in the two-ear mode while others cannot. According to the above model, the ability to hear beats in this mode should be better at low frequencies.

Is it so for you?

Identifying unknown frequencies

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

The phenomena of beats is at the root of how musical instruments such as pianos, guitars, violins etc are tuned. If you happen to play a musical instrument you may already be familiar with using a strobe tuner to tune an instrument, or tuning by ear to a reference tone. In either case you are making use of the beat frequency between the string you are tuning and the frequency to which you are tuning. When tuning by ear you listen for the beat frequency and adjust the tension in the string of your instrument until the beat frequency goes to zero.

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.

Submit your lab notebook

Make sure to submit your lab notebook by the end of the period. Download a copy of your notebook in PDF format and upload it to the appropriate spot on Canvas. Only one member of the group needs to submit to Canvas, but make sure everyone's name is on the document!

When you're finished, don't forget to log out of both Google and Canvas, and to close all browser windows before leaving!

Report: Summary and conclusions


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