Physics - Sound Wave Question with Solution | TestHub

Since, we know,

Frequency,$f=\frac{n}{2L} \sqrt{\frac{T}{m}}$

Where,$T=$tension in the string,

$L=$Length of the string

And$m=$linear mass density of the string.

$\therefore m=\frac{M}{L}=\frac{\pi {\left(\frac{D}{2}\right)}^2\cdot L\cdot \rho }{L}=\frac{\pi D^2\rho }{4}$

Thus,$f=\frac{1}{2L}\cdot \sqrt{\frac{T}{\frac{\pi D^2\rho }{4}}}$

For fundamental frequency,$n=1$

$f=\frac{1}{2L\frac{D}{2}} \sqrt{\frac{T}{\mathrm{\pi }\rho }}=\frac{1}{LD}\cdot \sqrt{\frac{T}{\mathrm{\pi }\rho }}$

$f\propto \frac{1}{LD}$