Born2bwire said:It first depends on what materials are involved, the medium in the hole and the material that the hole is cut out in. The simplest case is to assume air and a perfect electrical conductor (PEC) respectively. Regardless of the material, it comes down to the boundary conditions, the properties of the fields that have to be satisfied along any interface. For a PEC, the tangential electric and normal magnetic field components must be zero on the surface and all field values are zero in the interior of the PEC. Taken into context the fact that the fields must satisfy the wave equations inside the hole, this requires that only specific field configurations can be supported when passing through the hole. If we have a square hole, then the longest wavelength possible is one-half the width of the hole. This allows the field to always be zero at both edges since the field must be sinusoidal in the cross-sectional plane of the hole. (the edges are a nodal point of the tangential electric field).
So when waves pass through a hole, the hole will only support specific modes. Waves that are not of a supported mode (or a combination of modes) will be attenuated as they pass through the hole. The attenuation is dependent upon the frequency and thickness of the hole. For most holes or tunnels, the lowest supported mode is on the order of a wavelength but it depends on the actual geometries and materials involved. All of this is discussed in the confines of waveguides. Your holes and tunnels and such can be approximated as waveguides and you look them up for further clarification.
But yes, this is why if you enter a tunnely you will receive FM radio and not AM radio. This is a common homework problem in engineering EM courses. Though nowadays some of the nicer tunnels will have repeaters in the tunnel to reradiate the nonpropagating radio signals of interest.
The relationship between wavelength and hole diameter is based on the principle of diffraction, where light waves are bent as they pass through a small opening. As the wavelength of light decreases, the diffraction effect becomes more significant and the hole diameter needs to be smaller to achieve the same level of diffraction.
The size of the hole directly affects the wavelength of light passing through it. As the hole diameter decreases, the wavelength of light also decreases. This is because smaller holes cause more bending of light waves, resulting in a shorter wavelength.
Changing the wavelength of light will have a direct impact on the size of the hole required to achieve a certain level of diffraction. As the wavelength decreases, the hole diameter also needs to decrease in order to produce the same diffraction pattern.
The relationship between wavelength and hole diameter is important in various fields of research, such as optics, nanotechnology, and materials science. It is crucial in understanding the behavior of light and how it interacts with small structures, as well as in developing new technologies that utilize light and its properties.
Yes, the relationship between wavelength and hole diameter also applies to other types of waves, such as sound waves and water waves. This is because the principles of diffraction are applicable to all types of waves, where smaller openings cause more bending of the waves and result in shorter wavelengths.