Q. Consider a wire with density ( $d$ ) and stress (sigma). For the same density, if the stress increases 2 times, the speed of the transverse waves along the wire changes by

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Consider a wire with density ( $d$ ) and stress (sigma). For the same density, if the stress increases 2 times, the speed of the transverse waves along the wire changes by

Solution:

$because$ Speed of transverse wave

$v=sqrt{frac{text { Stress }}{text { density of wire }}}$ or $v=sqrt{frac{sigma}{d}}$

According to question, if $sigma$ increases 2 times

then $v_{1}=sqrt{frac{2 sigma}{d}}=sqrt{2} sqrt{frac{sigma}{d}}=sqrt{2} v$

Hence, speed of transverse waves along the wire changes by $sqrt{2}$ times.