How do wave effects depend on the size of the object with which the wave interacts? For example, why does sound bend around the comer of a building while light does not?

Diffraction is the bending of waves around obstacles or when they pass through an opening. The amount of diffraction that occurs depends on the size of the obstacle or the opening and the wavelength of the wave. In general, when the wavelength of the wave is much larger than the size of the obstacle or the opening, significant diffraction occurs, and the wave can bend around the obstacle.

Sound waves are mechanical waves that propagate through a medium (like air), and their wavelengths typically range from \(10^{-2}\) meters to \(10^1\) meters. Light waves, on the other hand, are electromagnetic waves that can travel through a vacuum, and their wavelengths are much smaller, typically ranging from \(10^{-9}\) to \(10^{-7}\) meters.

In the given example, we have a building (obstacle) and both sound and light waves interacting with it. Buildings are generally much larger than the wavelengths of both sound and light waves (at least in the order of \(10^1\) meters). However, the difference between the obstacle size and the wavelengths of sound waves is smaller than the difference between the obstacle size and the wavelengths of light waves.

In the case of sound waves, since their wavelengths are larger and closer in size to the dimensions of the building, significant diffraction can occur. This causes the sound waves to bend around the corner of the building and propagate further, making it possible for us to hear sounds from around the corner. On the other hand, light waves have much smaller wavelengths as compared to the size of the building. Consequently, there will be minimal diffraction of light waves when they encounter the building, and they mostly travel in straight lines with very limited bending. That's why we cannot see around the corner of a building with our eyes, as light does not bend around the obstacle as much as sound waves do. In summary, wave effects and their interaction with objects of different sizes depend on the wavelength of the waves and the size of the object. Sound waves can bend around corners of buildings due to their larger wavelengths and significant diffraction, while light waves do not bend as much, resulting in different behaviors for these two types of waves.