Question

the fundamental frequency of a string stretched with a weight of 4kg is 256 Hz. the weight required to produce its octave is? (ans :16 kg wt)

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{If}\mathrm{the}\mathrm{fundamental}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{spring}\mathrm{is}\mathrm{\nu }, \\ \mathrm{then}\mathrm{the}\mathrm{frequency}\mathrm{of}\mathrm{its}\mathrm{octave}\mathrm{is}2\mathrm{\nu }. \\ \mathrm{Hence},\mathrm{\nu }=\mathrm{K}\sqrt{\mathrm{T}}..........\left(1\right) \\ \mathrm{and}2\mathrm{\nu }=\mathrm{K}\sqrt{\mathrm{T}\text{'}}................\left(2\right) \\ \mathrm{from}\left(1\right)\mathrm{and}\left(2\right) \\ \mathrm{T}\text{'}=4\mathrm{T} \\ \mathrm{T}\text{'}=4\times 4=16\mathrm{kg}-\mathrm{wt} \end{gathered}$$