# Relationship between Wavelength and Frequency

We know that both the electric as well as magnetic fields travel in the form of waves and the disruption of these fields is called light. For example, when you throw a stone into a pool, we can notice the waves in a circular form that moves outward from the stone. Similar to these waves, every light ripple has a sequence of high points which is known as crests, wherever the electric field is maximum, and a sequence of low points is known as troughs, wherever the electric field is lowest. The distance among two wave crests is called wavelength and for troughs also it will be the same. The number of ripples that flow through a specified point within 1 sec is known as the frequency, and it is calculated in cycles/second known as HZ (Hertz). This article discusses the relationship between wavelength and frequency.

## Relationship between Wavelength and Frequency

The relationship between wavelength and frequency mainly discusses what is frequency, what is wavelength and its relationship.

### What is Frequency?

Frequency can be defined as the number of ripple oscillations for each unit time being calculated in Hz (hertz). The range of frequency heard by humans ranges from 20 Hz to 20000 Hz. If the sound frequency is above the range of human ears then it is known as ultrasound. Similarly, if the sound frequency is less than the range of human ears then it is known as infrasound.

The frequency (f) equation is = 1 / T

Where

f = Frequency

T = Time period

### What is Wavelength?

Wavelength (distance/length) can be defined as the distance between two close points within phase with each other. Therefore, two contiguous peaks otherwise trough on a ripple are separated through a distance of a single wavelength. The wavelength of a wave can be described with a symbol ‘λ’ lambda.

The wavelength is the distance between two crests or two troughs in a wave. The peak point of the wave is crest whereas the lowest point of the waveform is a trough. The units of wavelength are meters, cms, mms, nms, etc.

The wavelength (λ) equation is = λ = v/f

Where

V = Phase speed or velocity

f = Frequency

### How Wavelength & Frequency are Related?

The traveling of electromagnetic or EM waves can be done with a speed of 299,792 km/sec. This is one of the important characteristics. There are numerous types of waves are available which varies with frequency as well as wavelength. The light speed can be defined as the frequency of the EM wave is multiplies with its wavelength.

**Light speed = Wavelength * frequency of oscillation**

The above equation is used to discover the frequency or wavelength of the EM wave by dividing the measurement with the light speed to get another measurement.

### The Relation between Frequency and Wavelength

The relationship between wavelength and frequency of light can exist when a high-frequency wave travels faster than before on a rope. At some stage in this, we can observe that the wavelength turns into shorter. Thus, we have to know exactly is this relationship.

Another quantity is a period of time that can be used to illustrate a signal. It can also be defined when the time is taken for completing an oscillation. As frequency decides the number of times a wave oscillates and it can be expressed as,

**Frequency = 1/ T time period or f = 1/T**

Each position on the signal reaches to the same rate after a single period, as a signal goes through one oscillation throughout a single stage. This happens when every session result of oscillation travels through a wavelength distance within the single phase to close.

The speed of the wave (v) can be described as space traveled through a wave for each unit time. If believed that the signal travels a one wavelength distance within a single period,

**V = λ/T**

Therefore we know that T = 1/f, so the above equation can be expressed as,

**V = f λ**

The speed of the wave is equivalent to the product of its wavelength & frequency, which implies the association among these two.

### Relationship between Guided Wavelength and Cutoff Frequency

The relationship guided wavelength & cutoff frequency are discussed below.

#### Guide Wavelength

The guided wavelength can be defined as the space between two equivalent phase planes with the waveguide. This wavelength is a function used to operate frequency as well as the low-cutoff wavelength. The guide wavelength equation is shown below.

**λguide = λfreespace /√((1- λfreespace)/ λcutoff)2**

**λguide = c/f x1/√1-(c/2af)2**

This is mainly used while designing distributed formations within the waveguide. For instance, if we are designing a diode switch like a PIN diode using two shunt diodes with 3/4 wavelength spaces separately, utilize the guide wavelength (3/4) in your design. In a waveguide, the guided wavelength is longer comparing it in free space.

#### Cutoff Frequencies

There are different types of transmission modes that support a waveguide. But the normal transmission mode within rectangular waveguide is known as TE10. The upper cutoff wavelength or lower cutoff frequency used for this mode is extremely simple. The upper cutoff -frequency is accurately one octave over the lower.

λ upper cutoff = 2 x a

f_{lower cutoff }= c/2a (GHz)

a = broad wall dimension

c = light speed

The usual operation limits used for rectangular waveguide are ranges from 125% to 189% of the lower cutoff frequency. Therefore the cutoff frequency of WR90 is 6.557 GHz & the usual band of operation will range from 8.2 GHz to 12.4 GHz. The working of the guide will stop at the lower-cutoff frequency.

### Relationship between Speed of Sound Wavelength and Frequency

A sound wave travels at a particular speed and also it has properties like wavelength as well as frequency. The sound speed can be observed in a fireworks display. The blaze of a blast is observed well once its sound is clearly heard, the sound waves travel at a fixed speed which is much slower compared with light.

The sound frequency can be directly we can notice which is known as pitch. The sound wavelength is not straightly detected, however, indirect evidence is found within the connection of the musical instrument size along with the pitch.

The relationship between the speed of sound wavelength and frequency is the same for all waves

Vw = fλ

Where ‘Vw’ is the sound speed.

‘f’ is the frequency

‘λ’ is the wavelength.

Once the sound wave starts traveling from one medium to another medium then the sound speed can be changed. But, usually, the frequency remains very similar as it is similar to a driven oscillation. If ‘Vw’ alters & the frequency remains the same, after that the wavelength must be changed. When the sound speed is higher, then its wavelength is higher for a specified frequency.