Question

If the speed of the transverse wave in a wire under certain tension T is v, then its speed under tension $2T$ (in $ms^{-1}$) is

• A. $\frac{v}{\sqrt{2}}$
• B. $2v$
• C. $\sqrt{2}v$
• D. $\frac{3v}{\sqrt{2}}$
• E. $\frac{v}{2}$

Hint:

$v \propto \sqrt{T}$; doubling tension increases speed by a factor of $\sqrt{2} \approx 1.41$.

Answer 1

The Correct Option is C

Step 1: Concept
The speed $v$ of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$.

Step 2: Analysis
Speed is directly proportional to the square root of tension ($v \propto \sqrt{T}$).

Step 3: Calculation
If tension becomes $2T$, the new speed $v' = \sqrt{2} \times v$. Final Answer: (C)