Physics - Sound Wave Question with Solution | TestHub

For$\text{x}=\lambda$

$\frac{3\pi \text{x}}{2}=2\pi$

$\Rightarrow \lambda =\frac{4}{3}$

at x = 0

there is a pressure antinode. So first end must be close and in case of close at bot end

$l=\frac{\text{n}\lambda }{2}\Rightarrow l=\frac{2\text{n}}{3}$

for close at one end

$l=\left(2\text{n}+1\right)\frac{\lambda }{4}=\frac{\left(2\text{n}+1\right)}{3}$

So for close at one end possible lengths are

$\frac{\left(2\text{n}+1\right)}{3}=\frac{1}{3}\text{, }1\text{, }\frac{5}{3}\text{, }\frac{7}{3}$

Open at both ends is not possible for close at both end possible length are

$\frac{2\text{n}}{3}=\frac{2}{3}\text{, }\frac{4}{3}\text{, }2\text{, }\frac{8}{3}$...... so only possibility is (3)