A water wave with a wavelength of 35.6 cm approaches a wall with a large opening in it. The hole begins to close. What size does the hole in the wall need to be for the wave to noticeably diffract through the hole? Justify your answer.
12.8cm
To determine the size of the hole in the wall needed for the water wave to noticeably diffract through it, we need to consider the principle of diffraction.
Diffraction occurs when a wave encounters an obstacle or an opening that is comparable in size to its wavelength. In this case, the water wave has a wavelength of 35.6 cm. For diffraction to occur, the size of the hole should be similar to or smaller than the wavelength of the wave.
If the size of the hole is significantly larger than the wavelength of the water wave, it is less likely for diffraction to occur. The wave would simply pass through the opening without being significantly affected.
However, if the size of the hole is similar to or smaller than the wavelength, the wave will diffract through it. Diffraction causes the wave to spread out and bend around the edges of the opening, creating a pattern of interference and causing the wave to propagate into the region behind the obstacle.
Therefore, the hole in the wall needs to be approximately 35.6 cm or smaller in order for the water wave to noticeably diffract through it.