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Two progressive waves y(1) = 4 sin 500...

Two progressive waves ` y_(1) = 4 sin 500 pi t ` and ` y _(2) = 2 sin 506 pi t ` are superposed. Find the number of beats produced in one minute .

Text Solution

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Comparing the given equations with the standard equation y ` = A sin omega t ` , we have
` omega _(1) = 500 pi or, n_(1) = (omega_(1))/(2 pi) = (500 pi)/(2pi) = 250 ` Hz .
and ` omega _(2) = 506 pi or, n_(2) = (omega_(2))/(2 pi) = (506 pi) / (2 pi) = 253` Hz
`:. ` Number of beats per second
= difference in frequencies = 253 - 250 = 3
`:. ` Number of beats produced in one minute ` = 3 xx 60 = 180 ` .
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