## Noise Cancellation Technologies

### The Reason for Picking This Topic for My Project

It all started on a Saturday night, around 10 PM in my dorm room. My suitemate threw a birthday party for one of her friends. Of course, when there is a party, there is music and laughter. As I was in my room all these sounds were just noises to me. That's when I remembered one of Dr. Noe's many demonstrations: the tuning forks. Since the tuning forks were set at different frequencies, the sound waves from the tuning forks comes in and out of phase and where destructive interference occurs the sound is cancelled out. So I wondered if it was possible for me to build a device that cancels out noise.

After reading my email of my idea for the project, Dr. Noe mentioned the term ``noise cancellation device,'' and asked me to search for any information about it online. I immediately found a website with instructions on how to build noise-canceling headphones. This was the same site Dr. Noe had also found!

### Background Information on Interference

When two waves overlap, the combined intensity can either increase or decrease because of interference. Constructive interference occurs when waves of equal frequency are in phase. As a result of constructive interference the amplitude of the waves can add up. Destructive interference occurs when waves of equal frequency and amplitude are completely out of phase; then the waves cancel each other out. These two pictures show waves completely in phase and completely out of phase.

An interesting phenomenon that demonstrates constructive and destructive interference is the colors in soap films. As discussed in Eric Tompkins' report, when a soap film is held at almost a vertical position for several minutes, a white band and a black band forms at the top of the soap film. This effect is caused by interference of light reflecting off of two nearby surfaces: the outer surface and the inner surface of the soap film. Gravity causes the film to become ``wedge-shaped," in other words, thinner at the top. When the film becomes less than 10 nm thick then the phase change due to its thickness becomes insignificant, and the only phase change that remains is the 180 degree shift at the front surface. As a result, there is complete destructive interference of the two light waves and the surface looks black. When the thickness of film is around 100 nm, the additional phase shift due to the thickness creates constructive interference. As a result, all the colors reach a maximum intensity together, which explains the white band.

As I had mentioned before destructive interference is the basis of noise cancellation devices. One of those devices is a noise-canceling headphone. It has built-in microphones on the outside of each ear piece. The microphones detect noise then change it to an electrical signal that is out of phase with the actual noise. Therefore the sound you hear from the headphone is exactly out of phase with the actual sound, and together, there is silence.

However in reality the distance that the sound wave travels also affects the phase of the sound wave. That is why the noise canceling headphone works well with low frequency noise but not at high frequency.

### A Visual Demonstration of Phase Shifts

With Dr. Noe's help and his trusty oscilloscope I was able to get a visual picture of what really is happening. We worked with an oscillator, a small speaker, a microphone and of course an oscilloscope. An oscillator is an electronic device that generates signals. By connecting the oscillator to a speaker, we're able to generate sound and also the oscillator allows us to set the frequency and amplitude that we want. An oscilloscope is a graph-displaying device; it basically draws the graph of an electrical signal.

To demonstrate this concept of shift in phase of a sound wave with increasing distance we connected the oscillator to one channel of the oscilloscope and also to the loud speaker. The other channel of the oscilloscope was connected to the microphone. Then we watched the change in the oscilloscope display as we moved the microphone away from the speaker.

As the distance between the speaker and microphone increased the curve created by the microphone (the fuzzy one) moved to the right and got lower. The curve shifts to the right because it takes a longer time for the sound to reach the microphone, and it gets lower because the sound gets weaker when the microphone is further away. The nine pictures were taken over 3-4 seconds while the microphone was moving away from the speaker at a steady rate.

### Measuring the Velocity of Sound

Interestingly we can measure the velocity of sound by doing what we have been doing. However this time we'll need the help of a ruler. We moved the microphone away from the speaker until the fuzzy curve on the oscilloscope had shifted by one complete wavelength. We measured that distance to be 7.0 inches with an uncertainty of a quarter of an inch. The frequency is 2000 Hz; we know this because we can set it in the oscillator. Using the relationship

#### velocity   =   (frequency)(wavelength)

we found the velocity of sound to be 356 m/s. According to this speed-of-sound calculator, the speed of sound at 25 degrees C is 346 m/s. That number is pretty close to our measurement! Who could ever guess it is possible to measure the velocity of sound this way?!?!

### Making Standing Waves

By holding the speaker towards a wall we demonstrated standing waves. Standing waves are formed when the sound wave coming from the speaker reflects off the wall and interferes with the outgoing sound wave. Even if we moved the microphone like we did to demonstrate the phase shift previously, there was no phase shift! But we did see changes in the amplitude. The nodes (where the amplitude is the lowest) were actually 3-1/2 inches apart just as expected for a standing wave.

### Conclusion

I've learned from this project that to build a noise cancellation earphone requires a lot of work. The earphone has to be able to convert the noise into an electronic signal that is out of phase with the actual noise. However as we have discovered we have to also consider the distance between the microphone on the outside of the headphones and the loudspeaker on the inside. Depending on the frequency of the noise the phase can change significantly between these two places. It was also very interesting that we can find the velocity of sound, by using all we had. Although I had wished to make noise cancellation headphones myself, I still learned a lot about the concepts involved from this project.

Special thanks to Dr. Noe, for his patience, brilliant ideas and the many fascinating demonstrations he showed to us.