I am studying about continuous time periodic signal in that I saw some examples of sine waves and I have a question. The example is \$sin(400 \pi t)\$ is periodic or not. The explanation is given that sine wave repeats itself after every \$2\pi\$ interval. Now, If it is so than how to differentiate between frequency of two sine waves? I mean if it is \$sin(2\pi t)\$ or \$sin(400 \pi t)\$ no matter it will repeat after every \$2\pi\$. Can you please explain this issue? I also tried MATLAB for this issue.
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2\$\begingroup\$ No evidence of any research, such as Google. Question should be closed. \$\endgroup\$– Leon HellerCommented Jun 14, 2015 at 9:19
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1\$\begingroup\$ This has almost nothing to do with electronics, it is just basic trigonometry. \$\endgroup\$– LorenzoDonati4Ukraine-OnStrikeCommented Jun 14, 2015 at 9:37
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\$\begingroup\$ Use a frequency measuring device. \$\endgroup\$– Andy akaCommented Jun 14, 2015 at 9:39
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\$\begingroup\$ 'interval' is the periodic time, \$T\$, given by \$T=1/f\$ where \$f\$ is the frequency in Hz. Write your expression as \$sin(2\pi f t)\$ to find \$f\$ \$\endgroup\$– ChuCommented Jun 14, 2015 at 11:26
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2 Answers
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"The example is \$sin(400 \pi t)\$ is periodic or not" ... it is periodic, no qualification, no "or not".
And a sine wave repeats after every \$2 \pi\$ - yes.
Therefore \$sin(2 \pi t)\$ repeats when \$t=1\$ : so we call \$t=1\$ the period, or say the period is 1 second.
And \$sin(400 \pi t)\$ repeats when \$t=1/200\$, or repeats itself 200 times before \$t=1\$, so we call \$t=1/200\$ the period, or say the period is \$1/200\$ second.
That allows you to differentiate between the frequency of the two sinewaves. Frequency is simply the inverse of period:
\$1/1\$ second is called 1 Hz
\$1/200\$ seconds is called 200Hz
What more needs explaining?
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The statement "sine wave repeats itself after every \$2 \pi\$ interval" refers to the sine wave, defined by sin(t). You must always pay attention to the context in which such a statement is made, in particular note which (exact) meaning the words have.
answered Jun 14, 2015 at 9:54