Application+to+Sound+Waves

Sine Wave Application to Sound Waves A sound wave is basically a pressure oscillation in the air. At different frequencies(periods) the pitch of the sound will change, and the different amplitudes modify the intensity of the pressure oscillations which causes various volumes of sound. A sound wave's frequency is measured in Hz which is equal to Cycles/Second (or sinusoidal periods per second). For example, the middle C note on a piano is usually oscillating at a rate of 262Hz, or 262cycles/second. Now how does this apply to Noise Cancelling? So we know that 1 + -1 = 0 right? The same concept is used in various noise cancelling applications such as noise cancelling headphones or earphones. Basically, a microphone pickup on the outside of the headphones will input the sound into the headphone circuitry in the form of a sine wave.The internals will then create the sound of the inverse sine wave of the ambiant noise. Then this inverse sine wave will be played on top of the audio being played in the headphones, effectively canceling out ambient noise.

The Derivation of Equations for Middle C and the "Cancelling" version of Middle C:

Graphically, this is a Middle C:

Now to cancel out this theoretical ambient noise which is conveniently resonating at a constant middle C. We would have to invert the sine wave:



The equation that we have derived here are exact representations of our data because the data was exactly sinusoidal. But this equation is only true for the note C4, or middle C on a piano. The frequencies for higher notes are much higher and vice versa for lower notes; therefore the periods of the equations are smaller for the higher notes while the periods are longer for lower notes.

Fun FACT!: The frequency of the standard graph y=sinx is exactly 2pi Hz, and this is an extremely low frequency, here I have used wolfram alpha to compare it with other very low frequency audible noises.