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(B) Let the source be at $S$ and the observer at $O$. The direct distance $SO = 120\,m$.The ceiling is at a height $h = 25\,m$. The reflected wave tra

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$10, 5, \frac{10}{3}...... m$

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(B) Let the source be at $S$ and the observer at $O$. The direct distance $SO = 120\,m$.The ceiling is at a height $h = 25\,m$. The reflected wave travels from $S$ to the midpoint of the ceiling and then to $O$.Since the ceiling is at the midpoint,the horizontal distance from $S$ to the reflection point is $60\,m$ and from the reflection point to $O$ is $60\,m$.The path length of the reflected wave is $d = 2 	imes \sqrt{60^2 + 25^2} = 2 	imes \sqrt{3600 + 625} = 2 	imes \sqrt{4225} = 2 	imes 65 = 130\,m$.The path difference between the reflected wave and the direct wave is $\Delta x = 130\,m - 120\,m = 10\,m$.For constructive interference,the path difference must be an integer multiple of the wavelength: $\Delta x = n\lambda$,where $n = 1, 2, 3, \dots$.Thus,$10 = n\lambda \Rightarrow \lambda = \frac{10}{n}$.For $n = 1, 2, 3, \dots$,the possible wavelengths are $\lambda = 10\,m, 5\,m, \frac{10}{3}\,m, \dots$.

An observer receives waves directly from a source of sound distant $120\,m$ in a big hall. He also receives waves reflected from the mid-point of a $25\,m$ high ceiling. The wavelength of sound for constructive interference to take place between the two waves must be:

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