Question

If wavelength of a sound wave in a medium is reduced by 50% , what will be the percentage change in its frequency?

Answer 1

Dear Student
$$\begin{gathered} \lambda =\frac{v}{n} \\ Here\lambda iswavelength \\ visvelocityofsound \\ nisfrequency \\ Inonemediumspeedofsoundwillremaincons\tan t \\ Nowwhen\lambda isreducedby50\% \\ Newwavelength\lambda \text{'}=\lambda -\frac{50}{100}\lambda =\frac{1}{2}\lambda \\ Letn\text{'}isnewfrequencythen \\ \lambda \text{'}=\frac{v}{n\text{'}} \\ \frac{1}{2}\lambda =\frac{v}{n\text{'}} \\ n\text{'}=2\frac{v}{\lambda }=2n \\ Thepercentchangeinfrequency \\ \frac{n\text{'}-n}{n}\times 100=\frac{2n-n}{n}\times 100=100\% \end{gathered}$$
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