Question

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

• A. 1:1
• B. √2:1
• C. 1:√2
• D. 1:2

Answer 1

Answer: (C)

1:√2

Answer 2

The correct answer is (C) : $1:\sqrt2$
Given :
Tension in the string = T,
Mass per unit length = μ,
Velocity of transverse wave on a string , v = $\sqrt{\frac{\bar{T}}{\mu}}$
$v_1=\sqrt{\frac{T_1}{\mu}}$
$v_2=\sqrt{\frac{T_2}{\mu}}$
As per question T2 = 2T1
$\frac{v_1}{v_2}=\sqrt{\frac{\bar{1}}{2}}=\frac{1}{\sqrt2}$