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(B) When the piston is moved by a distance $\Delta x = 8.75 \, cm$,the path difference introduced in the reflected wave is $2 \Delta x$ because the wa

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$1000$

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(B) When the piston is moved by a distance $\Delta x = 8.75 \, cm$,the path difference introduced in the reflected wave is $2 \Delta x$ because the wave travels to the piston and back.Path difference $= 2 	imes 8.75 \, cm = 17.5 \, cm = 0.175 \, m$.For the intensity to change from a maximum (constructive interference) to a minimum (destructive interference),the path difference must be equal to an odd multiple of $\frac{\lambda}{2}$. The smallest change corresponds to $\frac{\lambda}{2}$.$\frac{\lambda}{2} = 0.175 \, m$$\lambda = 0.35 \, m$Using the wave equation $v = n \lambda$,we have:$n = \frac{v}{\lambda} = \frac{350 \, m/s}{0.35 \, m} = 1000 \, Hz$.

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