(1) The wavelength of the wave is 1.57 m.
(2) The velocity of the wave is 30 m/s .
(3) The frequency of the wave is 19.10 Hz and the time period of the wave is 0.052 s.
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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