Physics - Sound Wave Question with Solution | TestHub

Let the vibration takes place in the nth mode

So, for$1^{st}$case,$\frac{n\lambda }{2}=L$......(i)

And for$2^{nd}$case,$\left(n+1\right)\frac{{\lambda }^{\prime }}{2}=L$.....(ii)

From Equations. (i) and (ii), we get

$n\frac{\lambda }{2}=(n+1)\frac{\lambda \prime }{2}$$\left[\because \frac{\lambda }{2}=\mathrm{18\; cm} \mathrm{a}\mathrm{n}\mathrm{d}\frac{{\lambda }^{\prime }}{2}=\mathrm{16\; cm}\right]$

$\Rightarrow 18n=\left(n+1\right)16$

$\Rightarrow n=8$

So, minimum possible length$l=\frac{n\lambda }{2}$

$\Rightarrow l=8\times 18=144\mathrm{ cm}$