Answer:
Let L be the length of the air column For mode (a), \[L=3\lambda /4\] or \[\lambda =4L/3\] \[\therefore \] Frequency \[{{v}_{1}}=\frac{\upsilon }{\lambda }=\frac{3\upsilon }{4L}\] For mode (b), \[L=5\lambda /4\] or \[\lambda =4L/5\] \[\therefore \] Frequency \[{{v}_{2}}=\frac{\upsilon }{\lambda }=\frac{5\upsilon }{4L}\] Hence \[{{v}_{1}}.{{v}_{2}}=\mathbf{3:5}\]
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