Created By : Sunil Kumar Gandipadala

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 10, 2023

Simply take the advantage of our user-friendly and free Harmonic Wave Equation Calculator to find the displacement of an object along with the harmonic wave equation with the help of known values easily. Just enter your input amplitude, wavelength, velocity, time, initial phase, and distance from the source in the specified input boxes and hit the calculate to get the displacement value in a fraction of sections.

Initial phase:
Distance from the source:

Steps to Find Harmonic Wave

The following step by step process is useful to solve the harmonic wave equation questions. While solving the harmonic waves related problems refer to the following section.

  • Obtain amplitude, wavelength, time, wave velocity, wave initial phase and point position from the question.
  • Get the harmonic wave equation formula.
  • Substitute the given values in the above formula.
  • Perform the required math operations to get the displacement of the point.

Harmonic Wave Formula

In general, a wave is defined as a disturbance that spreads in space. When a wave occurs, the individual molecules oscillates back and forth. Harmonic wave maens all the particles are in simple harmonic motion.

The formula to determine the displacement of a point along the harmonic wave is follows:

y = A * sin[(2π / λ) * (x - vt) + Φ]


y is the displacement of a given point along the wave,

x is the position of that point (its distance from the source),

t is the time point,

v is the wave velocity,

λ is the wavelength,

A is the amplitude, and

Φ is the initial phase of the wave.


Question: Find the harmonic wave displacement of a point with an amplitude of 15 cm, the wavelength of 20 cm, velocity of 7 m/s, distance from the source is 5 cm, time is 10 sec, and initial phase of 12 radians.


Given that

Time point t = 10 s

Wave velocity v = 7 m/s

Distance from the source x = 5 cm

wavelength λ = 20 cm

Amplitude A = 15 cm

Initial phase of the wave Φ = 12 radians

The displacement of a point along the harmonic wave formula is y = A * sin[(2π / λ) * (x - vt) + Φ]

Put the values

y = 15 * sin[(2π / 20) * (5 - 7 * 10) + 12]

y = 15 * sin[(0.314) * (5 - 70) + 12]

= 15 * sin[(0.314) * (-65) + 12]

= 15 * sin[-20.41 + 12]

= 15 * sin(-8.41)

= 15 * (-0.849)

= -12.735

Therefore, the displacement of the point is -12.735 cm.

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FAQ's on Harmonic Wave Equation Calculator

1. What is a harmonic wave equation?

A harmonic wave is defined as the wave with a frequency that is a positive integer factor of the frequency of the fundamental frequency. The original wave is called the first harmonic wave.

2. What is the harmonic wave equation formula?

The parameters required to calculate the harmonic wave equation is amplitude, wavelength, velocity, time, and initial phase. The formula is y(x, t) = A * sin[(2π / λ) * (x - vt) + Φ].

3. What are the examples of harmonic waves?

The real-time examples of harmonic waves are music and acoustics, radio technology, electronic power transmission.

4. How to calculate the point displacement with a harmonic wave equation calculator?

You just need to provide all the known values in the input fields of the calculator and tap on the calculate button to check the displacement of a point along the harmonic wave with a detailed explanation.