Question 366: Waves

Question

In resonance tube, first and second resonance are obtained at depths $$22.7 \mathrm{~cm}$$ and $$70.2 \mathrm{~cm}$$ respectively. The third resonance will be obtained at a depth

Accepted Answer

First resonance will occur at $$l_1+\mathrm{x}=\frac{\lambda}{4}\quad$$ .... (i)
Second resonance will occur at $$l_2+\mathrm{x}=\frac{3 \lambda}{4}\quad$$ ..... (ii)
$$\begin{aligned}
& l_2+\mathrm{x}=3\left(l_1+\mathrm{x}ight) \
& l_2+\mathrm{x}=3 l_1+3 \mathrm{x} \
& 2 \mathrm{x}=l_2-3 l_1 \
& 	herefore \quad \mathrm{x}=\frac{l_2-3 l_1}{2} \
& \quad=\frac{70.2-68.1}{2}=1.05 \mathrm{~cm}
\end{aligned}$$
$$	herefore \quad$$ Third resonance occurs at $$l_3+\mathrm{x}=\frac{5 \lambda}{4}$$
$$\begin{aligned}
	herefore \quad l_3 & =5\left(l_1+\mathrm{x}ight)-\mathrm{x} \
& =5 l_1+4 \mathrm{x} \
& =113.5+4.2 \
& =117.7 \mathrm{~cm}
\end{aligned}$$

Answer

117.7 cm

Answer

92.9 cm

Answer

115.5 cm

Answer

113.5 cm

Waves

In resonance tube, first and second resonance are obtained at depths $22.7 \mathrm{~cm} and 70.2 \mathrm{~cm}$ respectively. The third resonance will be obtained at a depth

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