question_answer

Two transverse waves having amplitude 3 cm, frequency 50 Hz and wavelength \[\lambda ,\] moving in opposite directions are superimposed on fixed end of a steel rod of 5 cm whose other end is free. A stationary wave is setup in the rod with 3 node and 3 antinode points, then which of the following is correct statement?

A)  The wavelength of wave is 4 cm.

B)  The maximum displacement of free end of rod about mean position is 3 cm.

C)  Every point on rod performs SHM.

D)  maximum displacement of free end is zero.

Correct Answer: A

Solution :

Resultant wave, v Maximum displacement \[=2A=6\,cm\] Total length of rod \[\ell =\frac{\lambda }{2}+\frac{\lambda }{2}+\frac{\lambda }{4}=\frac{5\lambda }{4}\] \[\Rightarrow \]               \[\lambda =\frac{4\times 5}{5}=4\,cm\]