### 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 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.