A) 20, 20/3, 20/5 etc
B) 10, 5, 2.5 etc
C) 10, 20, 30 etc
D) 15, 25, 35 etc
Correct Answer: A
Solution :
Let \[S\] be source of sound and \[P\] the person or listner. The waves from \[S\] reach point \[P\] directly following the path \[SMP\] and being reflected from the ceiling at point \[A\] following the path \[SAP\]. \[M\] is mid-point of \[SP\] (i.e. \[SM=MP)\] and \[\angle \,SMA={{90}^{o}}\] Path difference between waves \[\Delta x=SAP-SMP\] We have \[SAP=SA+AP=2(SA)\] \[=\]\[2\sqrt{[{{(SM)}^{2}}+{{(MA)}^{2}}]}\] = \[2\sqrt{({{60}^{2}}+{{25}^{2}})}\]=130 \[m\] \[\therefore \] Path difference = SAP ? SMP \[=130-120=10\]m Path difference due to reflection from ceiling = \[\frac{\lambda }{2}\] \[\therefore \] Effective path difference Dx = \[10+\frac{\lambda }{2}\] For constructive interference \[\Delta x=10+\frac{\lambda }{2}=n\lambda \Rightarrow (2n-1)\frac{\lambda }{2}=10(n=1,\,\,2,\,\,3....)\] \[\therefore \] Wavelength \[\lambda =\frac{2\times 10}{(2n-1)}=\frac{20}{2n-1}\]. The possible wavelength are l\[=\]\[20,\,\,\frac{20}{3},\,\,\frac{20}{5}\,,\,\,\frac{20}{7}\,,\,\,\frac{20}{9}\,,\]?.. \[=\] \[20\]\[m\], \[6.67\]\[m\], \[4m,\]\[2.85\,m,\] \[2.22\]\[m,\]?..You need to login to perform this action.
You will be redirected in
3 sec