Question

A riverside warehouse has several small doors facing the river. Two of these doors are open as shown in the figure below. The walls of the warehouse are lined with sound-absorbing material. Two people stand at a distance L = 105 m from the wall with the open doors. Person A stands along a line passing through the midpoint between the open doors, and person B stands a distance y = 20 m to his side. A boat on the river sounds its horn. To person A, the sound is loud and clear. To person B, the sound is barely audible. The principal wavelength of the sound waves is 1.60 m. Assuming person B is at the position of the first minimum, determine the distance d between the doors, center to center.

Answer 1

From the figure:

\(\begin{aligned} \tan \theta &=\frac{y}{L} \\ &=\frac{20}{105} \\ \theta &=10.78^{\circ} \end{aligned}\)

The condition for the \(1^{\text {st }}\) minimumis, \(d \sin \theta=\frac{\lambda}{2}\)

\(\begin{aligned} d \sin (10.78) &=\frac{1.60}{2} \\ &=4.28 \mathrm{~m} \end{aligned}\)