# Relation Between Frequency And Wavelength

A wave is defined as a disturbance in a material that transports energy without causing net particle movement. They travel in a periodic, repeated motion, transferring energy from the source to the destination. Waves are divided into two types: transverse waves and longitudinal waves. Transverse waves are light and water waves while longitudinal waves are sound and compression waves.

**What is the frequency?**

The number of oscillations of a wave per unit of time is defined as frequency (Hz). It is the reciprocal of time and is represented by the sign f. Its unit of measurement is hertz. Its dimensional formula is [M^{0}L^{0}T^{-1}].

**What is wavelength?**

The distance between the two closest points in phase with each other is specified as a wavelength. It’s represented by the symbol (lambda). It is the product of a wave’s distance travelled per unit time and the total time taken. Its unit of measurement is meters. Its dimensional formula is written as [M^{0}L^{1}T^{0}].

**Relation Between Frequency And Wavelength**

The frequency and wavelength are indirectly proportional to each other. More is the wavelength, lesser is the frequency and vice-versa. The speed at which a wave travels is equal to the product of its frequency and wavelength, which justifies the link between these two parameters.

V = λ fwhere,

V is the wave speed,

f is the wave frequency,

λ is the wavelength.

**Derivation**

The relation between the frequency and wavelength can be derives using the formulas for these two quantities.

We know that frequency is the time taken to complete one oscillation out of time t. So we have,

f = 1/t …….. (1)

Also, it is known that the speed of a wave is the ratio of distance travelled by the wave to the total time taken by it.

V = λ/t

V = λ (1/t)

Using (1) we get,

V = λ f

This derives the relation between frequency And wavelength of a wave.

**Sample Problems**

**Problem 1. Calculate the wave frequency if a wave completes one cycle in 0.02 s.**

**Solution:**

We have,

Time (t) = 0.02 s

Using the formula we have,

f = 1/t

f = 1/0.02

f = 50 Hz

**Problem 2. Calculate the wavelength of a wave travelling at the speed of 250 m/s and has a frequency of 600 Hz.**

**Solution:**

We have,

V = 250,

f = 600

Using the formula we have,

V = λ f

=> 250 = λ (600)

=> λ = 250/600

=> λ = 5/12

=> λ = 0.416 m

**Problem 3. Calculate the wavelength of a wave travelling at the speed of 32 m/s and has a frequency of 800 Hz.**

**Solution:**

We have,

V = 32,

f = 800

Using the formula we have,

V = λ f

=> 32 = λ (800)

=> λ = 32/800

=> λ = 1/25

=> λ = 0.04 m

**Problem 4. Calculate the frequency of a wave travelling at the speed of 70 m/s and has a wavelength of 2 m.**

**Solution:**

We have,

V = 70,

λ = 2

Using the formula we have,

V = λ f

=> 70 = 2f

=> f = 70/2

=> f = 35 Hz

**Problem 5. Calculate the frequency of a wave travelling at the speed of 135 m/s and has a wavelength of 10 m.**

**Solution:**

We have,

V = 135,

λ = 10

Using the formula we have,

V = λ f

=> 135 = 10f

=> f = 135/10

=> f = 13.5 Hz

**Problem 6. Calculate the time taken by a wave for travelling a distance of 0.2 m at the speed of 350 m/s.**

**Solution:**

We have,

V = 350,

λ = 0.2

Using the formula we have,

V = λ f

=> 350 = 0.2 f

=> f = 350/0.2

=> f = 1750 Hz

Find the time taken by using the formula f = 1/t.

t = 1/f

= 1/1750

= 0.00057 s

**Problem 7. Calculate the velocity of a wave that travelled a distance of 2.5 m in 8 s.**

**Solution:**

We have,

λ = 2.5,

t = 8,

Find the frequency by using the formula,

f = 1/t

= 1/8

= 0.125 Hz

Using the formula we have,

V = λ f

V = (2.5) (0.125)

V = 0.3125 m/s

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