The linear density of a wire is 0 . 0 5g * cm^(-1) . The wire is stretched with a tension of4 . 5 xx 10^(7)dyn between two rigid supports . A drivingfrequency of 420 Hzresonatesthe wire. At the next higherfrequency of 490 Hz , another resonance is observed. Find out the length of the wire .

The linear density of a wire is 0 . 0 5g * cm^(-1) . The wire is stret

1.	The linear density of a wire is 0 . 0 5g * cm^(-1) . The wire is stretched with a tension of4 . 5 xx 10^(7)dyn between two rigid supports . A drivingfrequency of 420 Hzresonatesthe wire. At the next higherfrequency of 490 Hz , another resonance is observed. Find out the length of the wire .
Answer» <html><body><p></p>Solution :<a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> 420 Hz frequency ofthe p- th harmonic .<br/>So , <a href="https://interviewquestions.tuteehub.com/tag/490-318539" style="font-weight:bold;" target="_blank" title="Click to know more about 490">490</a> Hz = frequency of the (p + 1) - th harmonic .<br/>Then, 420 ` = (p)/(2l) sqrt((T)/(m)) and 490 = (p + 1) / (2l) sqrt((T)/(m))`<br/>`:. (420)/(490) = (p)/(p + 1) or , p = 6 `<br/>So , we get, ` 420 = (6)/(2l) sqrt((T)/(m))`<br/>or , `l = (6) /(2 xx 420) sqrt((4 . 5 xx <a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a> ^(7))/(0 . 0 5 )) = 214 . <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a> <a href="https://interviewquestions.tuteehub.com/tag/cm-919986" style="font-weight:bold;" target="_blank" title="Click to know more about CM">CM</a> `</body></html>