Frequency (f) and wavelength (λ) are two fundamental properties of waves that are related to each other in the context of wave physics.

**Frequency (f):****Definition:**Frequency refers to the number of oscillations or cycles of a wave that occur in a unit of time. It is measured in Hertz (Hz), where 1 Hertz is equivalent to 1 cycle per second.**Symbol:**$f$**Relationship with Period (T):**The frequency is inversely proportional to the period ($T$), where $T$ is the time it takes for one complete cycle. The relationship is given by $f=T1 $.

**Wavelength (λ):****Definition:**Wavelength is the distance between two consecutive points in a wave that are in phase (e.g., two consecutive peaks or troughs). It is usually measured in meters.**Symbol:**$λ$**Relationship with Wave Speed (v):**The wavelength is related to the wave speed ($v$) and frequency by the equation $v=fλ$. This equation shows that the speed of a wave is equal to the product of its frequency and wavelength.

**Relationship between Frequency and Wavelength:**- As mentioned in the previous response, there is an inverse relationship between frequency and wavelength for a wave traveling at a constant speed. Mathematically, the relationship is given by $v=fλ$, where $v$ is the wave speed.

In summary, frequency represents how many cycles of a wave occur in a given time, and wavelength is the distance between two corresponding points in a wave. The relationship between frequency and wavelength is essential in understanding wave behavior and is described by the wave equation.

**If Frequency Increases What Happens To Wavelength**

The relationship between frequency (f) and wavelength (λ) is described by the wave equation:

v=fλ

where:

- $v$ is the speed of the wave,
- $f$ is the frequency, and
- $λ$ is the wavelength.

If the frequency of a wave increases, and the speed of the wave remains constant, then the wavelength must decrease. This is an inverse relationship. Mathematically, you can see it in the equation: as $f$ increases, $λ$ decreases, and vice versa, as long as $v$ remains constant.

In simpler terms, when you have a higher frequency, the waves are closer together, resulting in a shorter wavelength. Conversely, lower frequency corresponds to longer wavelengths.