Two strings and of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed ‘ ‘ and on string with speed ‘ ‘. The ratio is
A)
B)
C) 2
D) 4

contexto.120

3 years ago

Answer is (C)
The velocity of wave travelling on string is
$\begin{array}{l} v=n \lambda=\frac{\lambda}{2 L} \sqrt{\frac{T}{\mu}}=\sqrt{\frac{T}{\mu}} \\ \because \quad n=\frac{1}{2 L} \sqrt{\frac{T}{\mu}} \\ \therefore \quad \quad \vee=\sqrt{\frac{T}{m \ell^{2}}} \Rightarrow v=\sqrt{\frac{T \times \ell}{m}} \\ Y=\frac{T \times \ell}{A \Delta L} \\ \therefore \quad T \times \ell=Y A \Delta L \\ \therefore \quad V=\sqrt{\frac{Y \cdot A \cdot \Delta L}{m}} \\ \therefore \quad V \propto \sqrt{A} \quad \text { (A is area) } \end{array}$
For string A, radius is , and for string B, radius is

is same for both and in is same for both.