An example of how waves can travel at different speeds is the phenomenon of refraction. Refraction occurs when a wave changes its speed and direction as it passes from one medium to another. The change in speed is caused by the change in the wave's propagation characteristics in different mediums.
One common example is the refraction of light waves as they pass through different substances, such as air, water, or glass. When light travels from one medium to another, such as from air to water, it undergoes a change in speed and direction. This change in speed is due to the variation in the optical density of the two mediums.
The speed of light in a medium is determined by its refractive index, which is a measure of how much the speed of light is reduced in that medium compared to its speed in a vacuum. When light waves encounter a boundary between two mediums, each with a different refractive index, they can bend or change direction.
For example, when light travels from air into water, it slows down because water has a higher refractive index than air. This change in speed causes the light waves to bend towards the perpendicular (normal) to the boundary between the two mediums. This bending is known as refraction.
The change in speed and direction of waves due to refraction is not limited to light waves but can also occur with other types of waves, such as sound waves or ocean waves. In each case, the specific properties of the mediums involved, such as their density or elasticity, determine how much the wave speed changes and the extent of the resulting refraction.