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» Solution :LET 420 Hz frequency ofthe p- th harmonic . So , 490 Hz = frequency of the (p + 1) - th harmonic . Then, 420 ` = (p)/(2l) sqrt((T)/(m)) and 490 = (p + 1) / (2l) sqrt((T)/(m))` `:. (420)/(490) = (p)/(p + 1) or , p = 6 ` So , we get, ` 420 = (6)/(2l) sqrt((T)/(m))` or , `l = (6) /(2 xx 420) sqrt((4 . 5 xx 10 ^(7))/(0 . 0 5 )) = 214 . 3 CM `