Harmonic Wave Equation Calculator
Simply use our user-friendly and free Harmonic Wave Equation Calculator to quickly determine an object's displacement as well as the harmonic wave equation using known values. Simply enter your input amplitude, wavelength, velocity, time, initial phase, and distance from the source in the designated input fields and press the calculate button to obtain the displacement value in fractions of sections.
Harmonic Wave Equation Calculator: Here's one of the simplest – to find out how far a point has moved along a harmonic wave as it travels through space. This tool might help you speed up your calculations and save time when determining the exact displacement of a point. The output portion of the calculator will give you the exact result as well as a full explanation of how to solve the problem. In the sections below, students can find solved examples and instructions for manually calculating point displacement.
What is a Harmonic Wave?
A wave is an acoustic disturbance that travels through space. Individual molecules wobble back and forth as it passes through space. If the wave is harmonic, all particles are moving in a basic harmonic motion.
Harmonic Waves Formula
A wave is a disturbance that propagates through space in general. Individual molecules oscillate back and forth when a wave arises. The particles in a harmonic wave are all moving in a basic harmonic motion.
The following is the formula for calculating the displacement of a point along with a harmonic wave: y = A * sin[(2π / λ) * (x - vt) + Φ]
- Where, y = displacement of a given point along with the wave,
- x = position of that point (its distance from the source),
- t = time point,
- v = wave velocity,
- λ = wavelength,
- A = amplitude, and
- Φ = initial phase of the wave.
Harmonic Wave Equation Examples
Question 1:Calculate the harmonic wave displacement of a point with an amplitude of 25 cm, a wavelength of 15 cm, a velocity of 8 m/s, a distance from the source of 7 cm, a time of 10 seconds, and an initial phase of 14 radians.
Solution:
Given:
Time point t = 10 s
Wave velocity v = 8 m/s
Distance from the source x = 7 cm
wavelength λ = 15 cm
Amplitude A = 25 cm
Initial phase of the wave Φ = 14 radians
Harmonic Wave Formula y = A * sin[(2π / λ) * (x - vt) + Φ]
y = 25 * sin[(2Ï€ / 15) * (7 - 8 * 10) + 14]
y = 25 * sin[(0.418) * (7 - 80) + 14]
= 25 * sin[(0.418) * (-73) + 14]
= 25 * sin[-30.51 + 14]
= 25 * sin(-16.51)
= 25 * (-0.284)
= -7.104
Hence, the displacement of the point is -7.104 cm.
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FAQs on Harmonic Wave Equation Calculator
1. What is the definition of a harmonic wave equation?
The wave has a frequency that is a positive integer factor of the fundamental frequency is known as a harmonic wave. The first harmonic wave is the initial wave.
2. How do you use a harmonic wave equation calculator to compute the point displacement?
To examine the displacement of a location along with the harmonic wave with a full explanation, simply enter all known numbers in the calculator's input fields and press the calculate button.
3. How do you find out how long a period is?
A periodic motion's time period is the amount of time that passes between two points where the motion is in the same position or phase. 2 pi/w = T
4. What are voltage harmonics, and what do they mean?
A sinusoidal wave with a frequency that is an integer multiple of the fundamental frequency is a harmonic of a voltage or current waveform in an electric power system.
5. In simple harmonic motion, how do you calculate the time interval?
x ( t ) = A cos ( ω t + ϕ ) This is the generalised equation for SHM. where, t represents time in seconds, is the angular frequency in inverse seconds, A represents amplitude in metres or centimetres and is the phase shift in radians