A) 2a
B) 8a
C) 4a
D) a
Correct Answer: B
Solution :
The energy of a wave travelling with velocity \[\nu \] is given by \[E=\frac{1}{2}m{{v}^{2}}\] Also \[\operatorname{y}=amplitude \,\times \, angular velocity\] \[\Rightarrow \,\,\,\,\nu =a\omega \] \[\therefore \,\,\,\,\,\,E=\frac{1}{2}m{{(a\omega )}^{2}}\] \[E=\frac{1}{2}m{{a}^{2}}{{\omega }^{2}}\] Also \[\omega =2\pi n\] where n is frequency. \[\therefore \,\,\,\,E=\frac{1}{2}m{{a}^{2}}{{(2\pi n)}^{2}}\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,E\propto {{a}^{2}}{{n}^{2}}\] It is given that energy remains the same. Hence, \[{{E}_{A}}={{E}_{B}}\] \[\therefore \,\,\,\,\,\,{{\left( \frac{{{a}_{A}}}{{{a}_{B}}} \right)}^{2}}={{\left( \frac{{{n}_{B}}}{{{n}_{A}}} \right)}^{2}}\] Given, \[{{n}_{A}}=n,\,\,\,{{n}_{B}}=\frac{n}{8}\] \[\therefore \,\,\,\,\,\,\,\,\frac{{{a}_{A}}}{{{a}_{B}}}=\frac{n/8}{n}=\frac{1}{8}\] \[\Rightarrow \,\,\,\,\,{{a}_{B}}=8{{a}_{A}}=8a\]
You need to login to perform this action.
You will be redirected in
3 sec
