steel wire $0.72\; m$ long has a mass of $5.0 \times 10^{-3}\; kg .$ If the wire is under a tension of $60\; N ,$ what is the speed (in $m/s$) of transverse waves on the wire?
steel wire $0.72\; m$ long has a mass of $5.0 \times 10^{-3}\; kg .$ If the wire is under a tension of $60\; N ,$ what is the speed (in $m/s$) of transverse waves on the wire?
Answer Mass per unit length of the wire,
$\mu =\frac{5.0 \times 10^{-3} \,kg }{0.72 \,m }$
$=6.9 \times 10^{-3} \,kg \,m ^{-1}$
Tension, $T=60 \,N$
The speed of wave on the wire is given by
$v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{60\, N }{6.9 \times 10^{-3} \,kg \,m ^{-1}}}=93 \,m \,s ^{-1}$
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- [IIT 2009]