What is the significance of the number 0.707 or 3dB or 1/sqrt(2)? I see it everywhere, e.g. bandwidth, quality factor, RMS, damping coefficient, and cutoff frequency. Are they all related somehow?
>>7961326
.707 = cos(45) = sin(45).
-3dB denotes the bandwidth of a signal. That's mostly convention but it is also proportional to [math] \frac{1}{2 \pi \tau} [/math].
>>7961338
Every constant is proportional to a constant.
>>7961338
>-3dB denotes the bandwidth of a signal
How so? Last time I checked it denoted an attenuation by the factor of 2^(-1) (or by the factor of 2 if speaking of power).
>>7961378
Cool dude.
Take an RC circuit, compute [math] \frac{1}{2 \pi RC} [/math] and look at the attenuation of a signal at that frequency, it will be -3dB.
>>7961338
>cos(45) = sin(45)
Stay pleb and keep using the noob degree scale instead of radian master race.
>>7961409
He was more likely to understand the significance of 45 degrees than [math] \frac{ \pi }{4} [/math] due to the fact that he had to ask this question in the first place.
>>7961326
The RMS of a sinusoid is the signals's amplitude divided by sqrt(2).
