A) \[\sqrt{2}:1\]
B) 2 : 1
C) 1 : 1
D) \[1:2\sqrt{2}\]
Correct Answer: D
Solution :
Idea Here, two concepts are used in this problem. One is of constraint motion and the other is of wave speed\[\left( v=\sqrt{\frac{T}{\mu }} \right)\] \[f=\frac{nv}{2L}\] For\[n=1\] \[{{f}_{1}}=\frac{v}{2L}\] \[\Rightarrow \]\[\frac{{{({{f}_{1}})}_{A}}}{{{\left( {{f}_{2}} \right)}_{B}}}=\frac{\sqrt{{{T}_{1}}/\mu }/2{{L}_{1}}}{\sqrt{{{T}_{2}}/\mu }/2{{L}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\times \frac{{{L}_{2}}}{{{L}_{1}}}\] \[=\sqrt{\frac{{{T}_{1}}}{2{{T}_{1}}}}\times \frac{1}{4}\]\[\left[ \because {{T}_{1}}=\frac{{{T}_{2}}}{2} \right]\] \[=\sqrt{\frac{1}{2}}\times \frac{1}{2}=\frac{1}{2\sqrt{2}}\] TEST Edge Questions based on standing waves on a string or in a organ pipe are usually asked in JEE Main.
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