How to Find Wavelength of Transverse Wave: Problems, Examples and Facts

The article discusses some facts on how to find wavelength of transverse wave along with examples and solved problems. 

The transverse wave possesses several maxima and minima above and below its mean position, respectively, depending on the particle’s displacement. The maxima are called the crest, whereas the minima are called the trough. The horizontal distance between two maxima or crests is the transverse wave wavelength.

The wavelength is the measure of the wave’s extent. It can be determined by estimating the horizontal distance between any two interconnected points on the wave, whether longitudinal or transverse. 

A wave transmits the energy from one position to another without fixed displacement of the particles of the medium where it propagates. The transverse wave emerges in a periodic or repeating pattern over time and space. “The length of the wave’s one repetition spatially known as wave cycle is the transverse wave wavelength.” 

Merely saying, the transverse wave wavelength is the total distance by a wave in one complete cycle (spatial repetition). Hence, the wavelength is found by calculating the horizontal distance between repeating units such as crest or trough in the wave pattern. 

Transverse Wave Wavelength
Transverse Wave Wavelength
(credit : shutterstock)
How to Find Wavelength of Transverse Wave
How to Find Wavelength of Transverse Wave

We can visualize the transverse characteristics when we plot the Displacement Vs. Distance graph for the vibrating or oscillating particles from their mean position. Plotting the displacement on the y-axis and the distance on the x-axis for the transverse wave enables us to find the wavelength. 

Displacement Vs Distance Graph
Displacement Vs Distance Graph

Suppose we have two transverse waves, the Displacement Vs. Distance graphs for both waves allow us to determine which wave has a longer wavelength and which one has a lower one. Of course, the longer wavelength has a maximum distance between two crests compared to shorter wavelengths. 

Transverse Wave Wavelength
Transverse Wave Wavelength

Read more about Transverse Wave.

How to Find Wavelength of Transverse Wave from below Displacement-Distance Graph?  

How to Find Wavelength of Transverse Wave
How to Find Wavelength of Transverse Wave

Solution

We observe that the shapes of both crests and troughs are symmetrical in a transverse wave. Hence, we can measure the distance between any two crests or troughs to find out their wavelength.

Let we choose the crests A and D.

Distance between crest A and D is 4m.

The wavelength of transverse wave is 4m.

How to Identify a Transverse Wave?

The propagated wave is identified as a transverse wave if:

  • It consists of several crests and troughs alternately. 
  • It was created when we stretched the flexible connectors like strings, ropes, etc. 
  • It propagated only in solid or liquid, not in gases. 
  • It does create pressure differences on the medium. 
  • It does not change the density of the medium. 

The waves set up the disturbance patterns when they move through the medium. Depending upon the direction of particles of the medium with respect to wave propagation, we can categorize the wave as longitudinal or transverse. When the particles vibrate perpendicular to the wave direction, the wave is identified as a transverse wave. 

Since the wave involves energy transport, it transmits energy to the particles of the medium. It charged the particles so that they could be displaced to oscillate up and down right angle to the wave direction. The vibration of particles provokes the formation of alternate crests and troughs in the transverse wave. That’s how the particle motion characterized the transverse wave. 

How to Identify Transverse Wave
How to Identify Transverse Wave
(credit: shutterstock)

The transverse waves primarily travelled in the solid medium rather than liquid since they require a relatively rigid medium to share their energy. When we stretch the string or ropes from both ends, it builds tension force on them, leading to the generation of a transverse wave. When we pluck the tightly tied string, it delivers a wave with the disturbance that travels along the entire string’s length and shares the energy among the particles of the string medium. 

The particles in the gas medium slip past each other as the medium is not rigid, stopping the particles from displacing their neighbor particle in a right angle to the energy transport. The reason the transverse is not propagated in the gas medium

Read more about Physical Properties.

Identify a Transverse Wave from below Diagrams

How to Identify Transverse Wave
How to Identify Transverse Wave
(credit: shutterstock)

Solution:

In diagram (a),

The wave consists of alternate crests and troughs, which occur when the particles vibrate perpendicular to wave propagation. Hence, it is a transverse wave. 

In diagram (b),

The wave consists of compression and expansion, which occurs when the particles vibrate parallel to the direction of wave propagation. Hence, it is a longitudinal wave. 

Transverse Wave Wavelength Formula

The transverse wave wavelength formula is acquired from the wave speed equation.

Since the transverse wave does not alter the density of the medium, the wave drives with the constant motion in it. So, the transverse wave speed reveals how much the wave traveled in unit time, whereas the distance travelled is the wavelength of the transverse wave.

The speed v of the transverse wave is the change in distance ∆x per unit time t.

v = Δx/t

Rearrange the above equation for writing the distance change ∆x formula,

Δx = vt

Transverse wave wavelength λ is the distance change ∆x between two crests or troughs per unit time period T.

λ = vT

But the time period and frequency are inversely proportional. i.e., f = 1/T

λ = v/f

The above is the transverse wave wavelength formula that calculates the distance traveled between two crests

Transverse Wave Wavelength Formula
Transverse Wave Wavelength Formula (credit: shutterstock)

Read more about Wavelength and Frequency.

What is the wavelength of a transverse wave that moves at 200m/s with the frequency of 50Hz? 

Given:

v = 200m/s

f = 50Hz

To Find:

λ =?

Formula:

λ = v/f

Solution:

The wavelength of transverse wave is calculated as,

λ = v/f

Substituting all values,

λ = 200/50

λ = 4

The wavelength of the transverse wave is 4m.

If light travels at 500m/s in 2ms, what is the wavelength of the light wave? 

Given:

v = 500 m/s

T = 2ms = 2×10-3

To Find:

λ =?

Formula:

λ  = v/f

Solution:

The wavelength of the light wave is calculated as,

λ  = v/f

Substituting all values,

λ   = 500 x 2 x 10-3

λ  = 1

The wavelength of the light is 1m.

From the Displacement Vs. Distance graph above for the transverse wave produced from the stretched string at 100Hz, find the wavelength value and calculate the speed of a transverse wave. 

Given:

f = 100Hz

From graph,

λ = 4m

To Find:

v =?

Formula:

λ = v/f

Solution:

The speed of transverse wave is calculated as,

λ = v/f

Rearranging for the speed v,

v = λf

Substituting all values,

v = 100 x 4

v = 400

The speed of the transverse wave of a stretched string is 400 m/s.

Read more about the Speed.


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