How does frequency determine a wave's penetration depth?

The frequency of a wave determines its penetration depth by affecting its absorption and attenuation in a medium.

In more detail, the penetration depth of a wave is the distance a wave can travel into a medium before its intensity is significantly reduced. This is largely determined by the frequency of the wave and the properties of the medium it is travelling through. The higher the frequency of the wave, the more energy it carries, and the more likely it is to be absorbed by the medium, reducing its penetration depth.

This is because waves with higher frequencies have shorter wavelengths. When a wave encounters a medium, it interacts with the particles in that medium. If the wavelength of the wave is shorter (i.e., the frequency is higher), it will interact with more particles in a given distance, leading to more absorption and less penetration.

This principle is evident in many areas of physics. For example, in electromagnetic waves, higher frequency waves like X-rays and gamma rays can penetrate materials that lower frequency waves like visible light and radio waves cannot. This is because the higher frequency waves have more energy to overcome the absorption by the material.

Similarly, in acoustics, lower frequency sound waves can penetrate further into materials than higher frequency waves. This is why you can hear the bass from a loud music even if you are far away from the source or behind a wall - the low frequency sound waves are able to penetrate the wall and travel further.

However, it's important to note that the relationship between frequency and penetration depth is not always straightforward. The properties of the medium, such as its density and composition, also play a significant role. For instance, certain materials may have 'resonant frequencies' at which they absorb more energy, reducing the penetration depth at those specific frequencies.

IB Physics Tutor Summary: In simple terms, a wave's penetration depth decreases as its frequency increases. Higher frequency waves carry more energy and get absorbed more by materials they pass through, reducing how far they can go. However, the material's characteristics also influence how deep a wave can penetrate, including specific frequencies where a material absorbs more energy.