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» <html><body><p></p>Solution :In the <a href="https://interviewquestions.tuteehub.com/tag/present-1163722" style="font-weight:bold;" target="_blank" title="Click to know more about PRESENT">PRESENT</a> <a href="https://interviewquestions.tuteehub.com/tag/case-910082" style="font-weight:bold;" target="_blank" title="Click to know more about CASE">CASE</a>, <a href="https://interviewquestions.tuteehub.com/tag/frequency-465761" style="font-weight:bold;" target="_blank" title="Click to know more about FREQUENCY">FREQUENCY</a> of `<a href="https://interviewquestions.tuteehub.com/tag/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>^(th)` harmonic <br/> `f _(n) = n f _(1) = 420 Hz` <br/> `f _(n +1) = (n +1) f _(1)= 490 Hz `<br/> Taking subtraction, `n f _(1) + f _(1) -nf _(1) = 490 -420` <br/> `therefore f _(1) = 70 Hz` <br/> `therefore (1)/(2L) sqrt ((T)/( mu ))=70`<br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P2_C15_E02_051_S01.png" width="80%"/> <br/> `therefore L = (300)/(140) =2.1428 m ~~2.143 m`</body></html>