For one wire tied at both the ends with a tension of 450 N, linear density of mass is 0.05 g/cm. It sounds resonantly for two consecutive frequencies 420 Hz and 490 Hz. Find length of this wire.

For one wire tied at both the ends with a tension of 450 N, linear den

1.	For one wire tied at both the ends with a tension of 450 N, linear density of mass is 0.05 g/cm. It sounds resonantly for two consecutive frequencies 420 Hz and 490 Hz. Find length of this wire.
Answer» Solution :In the PRESENT CASE, FREQUENCY of `N^(th)` harmonic `f _(n) = n f _(1) = 420 Hz` `f _(n +1) = (n +1) f _(1)= 490 Hz ` Taking subtraction, `n f _(1) + f _(1) -nf _(1) = 490 -420` `therefore f _(1) = 70 Hz` `therefore (1)/(2L) sqrt ((T)/( mu ))=70` `therefore L = (300)/(140) =2.1428 m ~~2.143 m`