A plane wave has equation; y= 25sin(120 _4x).find the: (1)wave length (2)wave velocity (3)frequency and period of the wave

Note: The given equation seems to be incomplete. Most probably the equation was y=25sin(120t-4x). And the standard system of units (i.e. kg, m, s) is used.

Wavelength: The distance between the consecutive crest or trough of a wave is called the wavelength of a wave.

The equation of a plane wave oscillating in the y direction and traveling in the x direction is given by the equation,

y=A sin(ωt-kx)

where y is the displacement along the y direction, A is the amplitude of the wave, ω is the angular frequency, t is the time, x is the displacement along the x direction, and k is the wave constant.

The given equation is,

y=25sin(120t-4x)

Comparing this equation with the above equation, following values are obtained.

k= 4 m^(-1)

ω =120 rad/s

A=25

The wavelength λ is given by the formula,

λ=2π/k

Here k = 4 m^(-1), so

λ=2π/4

λ=1.57 m.

Velocity: The velocity of a wave is the product of the frequency and the wavelength.

The velocity v is given by the formula,

v=ω*λ/2π

Here ω=120 rad/s and λ=1.57 m, so

v=120*1.57/2π

v=30 m/s

Frequency: The number of oscillations completed in one second is called the frequency of a wave.

The formula of the frequency is,

f=v/λ

Here v=30 m/s and λ=1.57 m, so

f=30/1.57

f=19.10 Hz

Time period: The time taken to complete one cycle of oscillation is called the time period of oscillation.

The formula to calculate the time period T is,

T=2π/ω

Here ω=120 rad/s, so

T=2π/120

T=0.052 s.

Learn more about velocity of wave.

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