Question

The velocity of a transverse wave in a stretched wire is $100m{s}^{-1}$. If the length of wire is doubled and tension in the string is also doubled, the final velocity of the transverse wave in the wire is

• A. $100m{s}^{-1}$
• B. $141.4m{s}^{-1}$
• C. $200m{s}^{-1}$
• D. $282.8m{s}^{-1}$

Answer 1

Answer: (B)

$141.4m{s}^{-1}$

$v=\sqrt{\frac{T}{massperunitlength}}=100m/s$
when tension is double $T$ becomes $2T$ and mass per unit length remains same
so, $v_1=\sqrt{\frac{2T}{massperunitlength}}$
$=\sqrt{2}\times \sqrt{\frac{T}{massperunitlength}}$
$=\sqrt{2}\times 100$
$=141.4m/s$