A) \[\lambda =\frac{\pi {{x}_{0}}}{4}\]
B) \[\lambda =2\pi {{x}_{0}}\]
C) \[\lambda =\frac{\pi {{x}_{0}}}{2}\]
D) \[\lambda =4\pi {{x}_{0}}\]
Correct Answer: C
Solution :
We have the longitudinal wave given by \[x={{x}_{0}}\sin [2\pi (nt-x/\lambda )]\] \[={{x}_{0}}\sin \left( 2\pi nt-\frac{2\pi }{\lambda }x \right)\] The maximum particle velocity \[=A\omega =-{{x}_{0}}(2\pi n)\] The wave velocity \[=n\lambda \] Here we compare the given equation with the equation \[x={{x}_{0}}\sin (\omega t\pm kx)\] From the question, \[2\pi n{{x}_{0}}=4n\lambda \] \[\Rightarrow \] \[\lambda =\frac{\pi }{2}{{x}_{0}}\]
You need to login to perform this action.
You will be redirected in
3 sec
