Here's how the wavelength of waves changes with frequency when their speed remains constant:

The Relationship

* Inversely Proportional: Wavelength and frequency are inversely proportional. This means that as one increases, the other decreases.

The Formula

This relationship is captured in the following formula:

* v = fλ

Where:

* v = speed of the wave

* f = frequency of the wave

* λ = wavelength of the wave

Explanation

Imagine a wave moving like a ripple in a pond. The frequency represents how many ripples pass a certain point per second. If you increase the frequency, you are essentially squeezing more ripples into the same amount of time. To do this, the wavelength (the distance between two consecutive ripples) must decrease.

Example

Let's say you have a wave traveling at a constant speed of 10 meters per second. If you increase the frequency from 2 Hz to 4 Hz, the wavelength will need to decrease to maintain the same speed.

* Initial Calculation: λ = v/f = 10 m/s / 2 Hz = 5 meters

* Final Calculation: λ = v/f = 10 m/s / 4 Hz = 2.5 meters

In summary: When the speed of a wave is constant, increasing the frequency will result in a shorter wavelength.