Wave Mechanics Question 743
Question: Transverse waves of same frequency are generated in two steel wires A and B. The diameter of A is twice of B and the tension in A is half that in B. The ratio of velocities of wave in A and B is
[KCET 2001]
Options:
A) $ 1\ :\ 3\sqrt{2} $
B) $ 1\ :\ 2\sqrt{2} $
C) $ 1\ :\ 2 $
D) $ \sqrt{2}\ :\ 1 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ v=\sqrt{\frac{T}{m}}=\sqrt{\frac{T}{\pi r^{2}\rho }} $
$ v\propto \frac{\sqrt{T}}{r}\Rightarrow \frac{v _{A}}{v _{B}}=\sqrt{\frac{T _{A}}{T _{B}}}.\frac{r _{B}}{r _{A}}=\sqrt{\frac{1}{2}}.\frac{1}{2}=\frac{1}{2\sqrt{2}} $
BETA
