The medium a wave travels through significantly affects its wavelength by altering its speed while its frequency remains constant.
Understanding the Effect of Medium on Wavelength
When a wave moves from one medium to another, its speed changes. This change in speed is a fundamental property dictated by the characteristics of the new medium, such as density, elasticity, or refractive index. However, the wave's frequency, which is determined by the source creating the wave (like a vibrating object or an oscillating electric charge), does not change when it enters a different medium.
The relationship between a wave's speed, frequency, and wavelength is described by the fundamental wave equation:
The Wave Equation
The speed of a wave ($v$) is the product of its frequency ($f$) and its wavelength ($\lambda$):
$v = f\lambda$
This equation shows how these three properties are interconnected.
How Speed Changes Lead to Wavelength Changes
Since the frequency ($f$) stays constant when a wave enters a new medium, and the speed ($v$) changes due to the properties of that medium, the wavelength ($\lambda$) must also change to maintain the equality in the equation $v = f\lambda$.
As highlighted in the reference: a change in speed results in a change in wavelength.
More specifically:
- If the wave's speed decreases in the new medium (e.g., light moving from air to water or glass), its wavelength will decrease proportionally ($v \propto \lambda$ when $f$ is constant).
- If the wave's speed increases in the new medium (e.g., sound moving from air to a solid), its wavelength will increase proportionally.
Therefore, the medium affects wavelength indirectly by directly affecting the wave's propagation speed.
Practical Examples
This effect is observable in various wave phenomena:
- Light: When light enters a denser medium like water or glass from air, its speed decreases, causing its wavelength to shorten. This change in speed and wavelength is responsible for phenomena like refraction (the bending of light). The color of light, determined by its frequency, remains the same.
- Sound: When sound travels from one material to another (e.g., from air to water or vice versa), its speed changes based on the new medium's properties. Consequently, its wavelength changes, even though the pitch (frequency) remains the same.
In summary, the medium plays a crucial role in determining a wave's wavelength because it dictates the wave's speed while the frequency, set by the source, stays constant.
