Consider the following graph, showing two sine-wave signals like you will see fr

Question

Consider the following graph, showing two sine-wave signals like you will see from microphones, positioned in front of a speaker.

1. Note that the horizontal scale is in ms units. What is the frequency of the signals? (Note that we expect a unit.) f =

2. If the speed of sound is 339 m/s, what is the wavelength of the sound wave? ? =

3. The two signals differ by a phase. What is it, expressed in degrees? What is it, expressed in radians?

4. When the two microphones are at the same distance from the speaker, the two signals are in phase, lie on top of each other. For the phase difference shown, what is the minimum distance between the two microphones? Dmin =

Explanation / Answer

For Red Graph

Time period is from peak to peak

Time period = 0.125 ms

f = 1/T = 8 KHz

For Blue Graph

Time period is from peak to peak

Time period = 0.125 ms

f = 1/T = 8 KHz

Frequency = speed / wavelength

Wavelenth = 4.238 cm

For Red : Y = cos(2*pi*f*t)

For Blue : Y = sin(2*pi*f*t)

Phase diff = 90 Degrees or Pi/2 radians

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