A music practice room has an entrance consisting of two doorways, each 1.1 m wide and separated by a distance of 3.1 m. Outside the practice room, a tuning fork is struck in the hallway, producing a sound wave with a frequency of 512 Hz.

(i) Find all the angles of θ at which no sound will be heard within the practice room when the tuning fork is struck.

(ii) If a student is standing inside of the practice room as illustrated below when the tuning fork is struck outside of the room, will the student have a good explanation for not hearing the sound? Explain.

Assuming that the speed of sound is 340 m/s and that it has not bounced off the walls inside of the room.

Imagine that you are performing an experiment to study double-slit interference patterns. You have a setup where the distance "d" between the slits is much larger than the wavelength "λ" of the light passing through them. Calculate the angular full width value at the half maximum point of the central peak in the interference pattern based on this particular setup.

A 580 nm light beam source is used for a double-slit experiment. The slits have a separation of 0.35 mm, while the screen is located 1.6 m from the slits. The central maximum is located at the origin point of the coordinate system. One of the slits is covered with a thin sheet of transparent polythene material. Light will travel slower through this material medium compared to air; therefore, the waves passing through the polythene will be slowed down by 4.5 × 10^-16 s relative to the other slit. Express the value of this delay as a percentage of the wave's period.

Two slits are separated by a distance of "y" mm. Light of a wavelength (y/250) mm is used to illuminate the two slits. Calculate the angle (in units of degrees) between the two consecutive bright fringes produced by the interference pattern.

In Young's experiment, the slits are illuminated with coherent light of wavelength 632 nm. Careful measurement reveals the distance between the adjacent dark fringes to be 4.3 mm. If the screen is 2.2 m from the light source, what should be the slit separation?

An aperture is illuminated with a beam of light of wavelength 550 nm. The light intensity pattern observed on a screen positioned 2.0 m behind the aperture is shown below. Identify the type of the aperture based on the observed pattern.

A single slit diffraction pattern is observed on a screen placed at a distance d behind a 375 μm narrow slit. The light used has a wavelength of 560 nm. The observed intensity pattern is shown in the figure below. Determine the distance d.

In a water park, surface waves are generated in a large swimming pool and propagate at a speed of 0.2 m/s. A 5.0 m wall stands in the pool perpendicular to the direction of propagation of the waves and has an opening in its center. Using a wave profile device, you measure that every 30 seconds, 45 wave crests strike the wall. You also notice that no waves reach the opposite side of the swimming pool, 4.0 m away from the wall, at a position of 0.40 m from the point directly opposite the opening. However, waves do reach the opposite side everywhere within this distance. Determine the width of the wall opening.