A string of length L and mass M hangs freely from a fixed point. Then, the velocity of transverse waves along the string at a distance\[x\] from the free end is
A)\[gx\]
B)\[\sqrt{gx}\]
C) \[gL\]
D) \[\sqrt{gL}\]
Correct Answer:
B
Solution :
Total length of string\[=L\] Mass of the string\[=M\] The velocity of transverse wave\[v=\sqrt{\frac{T}{m}}\] where,\[T=\]weight of part of string hanging below the point under consideration. \[=\left( \frac{M}{L} \right)xg\] \[\Rightarrow \] \[v=\sqrt{\frac{\left( \frac{M}{L} \right)xg}{\left( \frac{M}{L} \right)}}=\sqrt{xg}\]