Harmonic Wave Equation Calculator, Formula, Calculation With Example

Harmonic Wave Equation Calculator :

Harmonics are used in music and acoustics, electronic power transmission, radio technology, etc. Enter the amplitude, wavelength, speed, and time into the harmonic wave equation calculator below.

Harmonic Wave Equation Calculator

Harmonic Wave Equation Calculator formula :

Displacement of a given point along the wave Y(cm) in centimeter is equal to the product of the amplitude A(cm)  in centimeter is multiply by the 2π is divided by the wavelength λ(cm) in centimeter is multiply by the position of that point x(cm) in centimeter is subtracted by the wave velocity v(m/s) in meter per second is multiply by the time point t(s) in second is the addition of the initial phase of the wave Φ(r) in radians.

Y(cm) = A(cm) * sin [(2π / λ(cm) ) * ( x(cm) – v(m/s) t(s) ) + Φ(r)]

where ,

y →displacement of a given point along the wave  in cm

x → position of that point ( its distance from the source) in cm

t → time point in sec

v → wave velocity in m/s

λ → wavelength in cm

A → amplitude in cm

Φ→ initial phase of the wave In rad

Example1 :

Calculate the harmonic wave displacement of a point with an amplitude of 20 cm , the wavelength 25cm ,velocity of 8m/s, distance from the source is 6cm time in 11 sec and initial phase of 13 radians?

Solution :

Time point t = 11 s

Wave velocity v = 8 m/s

Distance from the source x= 6 cm

Wavelength λ = 25 cm

Amplitude A = 20 cm

Initial phase of the wave Φ =13 radians

y = A * sin [(2π / λ) * ( x –vt ) + Φ]

y = 20 * sin [(2 π / 25) * (6 – 8 * 11) +13 ]

y = 20 * sin [ (0.251) * (6 – 88)+13]

y = 20 * sin [(0.251) * – 82+ 13]

y = 20 * sin [-20.58+13]

y = 20 * sin[-7.58]

y = 20 * ( -0.962)

y = -19.24 cm

Therefore , the displacement of the point is -19.24 cm.

Example2 :

Calculate the harmonic wave equation of a wave with an amplitude of 12 ,wavelength of 20 , velocity of 5 m/s , distance from the source is 5cm , time of 6 sec , initial phase of 10 degrees?

Solution :

y = A * sin [(2π / λ) * ( x –vt ) + Φ]

y = 12 * sin [(2 * 3.14 / 20 ) * ( 5- 5* 6 ) + 10]

y = 3.1251.

Leave a Comment