Question

A piano wire weighing 6.00 g and having a length of 90.0 cm emits a fundamentals frequency corresponding to the "Middle C” (v = 261.63 Hz). Find the tension in the wire.

• A. 1000 N
• B. 2.8 N
• C. 1480 N
• D. 2000 N

Answer 1

The correct option is C

1480 N

we know fundamental frequency $f=\frac{v}{2L}$ here $v=\sqrt{\frac{T}{\mu }}$ given $m=6g=6\times {10}^{-3}kg$

$L=90cm=0.9m$

$\mu$ = mass per unit length $=\frac{6\times {10}^{-8}}{0.9}$

Also,as $f=261.63Hz$ (given)

$\frac{v}{2L}=261.63Hz$

$\sqrt{\frac{T}{\mu }}\times \frac{1}{2L}=261.63$

$\sqrt{\frac{T}{\mu }}=261.63\times 2\times 0.9$

$\frac{T}{\mu }=(261.63\times 2\times 0.9{)}^2$

$T=(261.63\times 2\times 0.9{)}^2\times \frac{6\times {10}^{-3}}{0.9}$

$=1480N$