Example Wavelength Formula in In physics

However, the relationship between wavelength and frequency is inversely proportional, meaning that the greater the frequency, the shorter the wavelength.

Wavelength Formula

In physics, wavelength is defined as the distance a wave travels in one period. Wavelength is symbolized by the Greek letter, lambda (λ).

How to calculate the wavelength formula depends on the type of wave. Quoted from the book Memorization of High School Physics Formulas for Classes

1. Types of waves based on the medium they propagate

·         Mechanical Waves

Mechanical waves are waves whose propagation requires a medium. For example, sound waves and string waves.

·         Electromagnetic wave

Electromagnetic waves are waves whose propagation does not require a medium. For example, light waves.

2. Types of waves based on the direction of vibration and propagation

·         Transverse Waves

Transverse waves are a type of wave whose direction of vibration is perpendicular to the direction of propagation. For example, light waves and string waves.

·         Longitudinal Waves

Longitudinal waves are a type of wave whose direction of vibration is in the same direction as the direction of propagation. For example, sound waves.

So, what is the wavelength formula for these two types of waves? Read the following explanation complete with example questions and discussion.

Transverse Wavelength Formula

Wavelength Formula Illustration (zenius.com)

In transverse waves, the wavelength is the distance from the crest (hill) of the wave to the crest of the next wave or the trough of the wave to the trough that follows it. Simply put, 1 wavelength is 1 hill + 1 valley.

Mathematically, the lambda formula for transverse waves can be described as follows:

λ = s/n

Information:

λ = wavelength
s = distance traveled by the wave (m )
n = number of waves

Longitudinal Wavelength Formula

Longitudinal waves are calculated based on wave density and spacing. In one longitudinal wavelength there is 1 density and 1 sparseness.

So, the Lambda formula can be calculated based on the speed of propagation and wave period. Here’s the formula:

λ = v/f
orλ = vx T

Information:

v = speed of wave propagation (m/s)
λ = wavelength (m)f = wave frequency (Hz)T = wave period (S)

Formula for the Relationship between Wavelength and Frequency

Because frequency is related to determining the number of waves in a unit of time, there is a formula to calculate it. This wavelength is equal to the wave speed divided by the frequency of the wave which is stated in the formula λ = speed of light (c) : frequency (f)

Meanwhile, the units of each symbol are:

λ = meter (m)
C = speed of light in vacuum or speed of sound in airF + hertz (Hz)

Example Questions and Discussion of the Wavelength Formula

Sound Formulas (Handbook Glossary of Mathematical Formulas – Middle School Physics: Mathematical Formulas – Middle School Physics)

To make it easier to understand, the following is an example of a wavelength question along with its discussion, quoted from the books Quick & Easy Ways to Master Middle School Physics by Hendri Hartanto and Super Smart Master Middle School/MTs Mathematics and Science by Ratna Rima Melati:

1. A rope is 5 meters long, then vibrates 3 hills and 2 valleys of waves. Then the wavelength of the string is:

Given:
s = 5 mn = 5/2 = 2.5 waves (2 hills and two valleys)

Answer:

n.λ = s
λ = s/n= 5/2.5= 2 meters

2. A string is vibrated with a wave frequency of 10 Hz. If the wave travels at a speed of 30 m/s, what is the wavelength?

Known:
v = 30 m/sf = 10 Hz

Answer:

λ = v/f
= 30 m/s / 10 Hz= 3 m

3. A string is vibrated to form 1 ½ waves. If the distance traveled by the wave is 9 cm, calculate the wavelength!

Given:
s = 9 cmn = 1 ½ or 1.5

Answer:

λ = s/n
= 9/1.5= 6 cm

4. A longitudinal wave travels 10 cm in 2 seconds. Calculate the wavelength:

It is known:
s = 10 cmn = ½ = 0.5 waves (because at a distance s = cm there is only 1 density)

Answer:

λ = s/n
= 10 cm/0.5= 20 cm

5. A wave has a frequency of 200 Hz with a propagation speed of 20 m/s. What is the wavelength?

Known:
f = 200 Hzv = 20 m/s

Answer:

λ = V/f
= 20/200= 0.1 meters

6. A wave has a wavelength of 0.2 meters with a period of 60 seconds. What is the speed of propagation of the wave?

Known:
λ = 0.2 mT = 60 s

Answer:

λ = c/f
0.2 = c/60c = 0.2/60c = 12 m/s

7. One end of a string is tied, while the other end is vibrated up and down with a period of 0.2 s to form two hills and a valley. If the distance between the vibrator and the binding post is 1.5 m, determine the speed of the wave formed!

Known:
T = 0.2 s

Answer:

T = 1/ƒ
0.2 = 1/ƒƒ = 5 Hz

This is a complete explanation of the wavelength formula along with example questions. Please remember, the wavelength formula can be used according to the type of wave.