The equation y=25sin(120t-4x) represent a Wave motion.Determine the frequency and period
The general equation is
y(x,t)= Amplitude*sin(2PIx/lambda +- w*t) - sign going in x direction, + sign going in -x direction.
putting your given equation in this form...
w=4
2PIf=4
f=pi/4 hz
period= 1/f= 4/PI sec
SOLVE IT PLEASE
To determine the frequency and period of the given equation y = 25sin(120t - 4x), we need to understand the relationship between the standard form of a sine wave equation and the frequency and period.
The standard form of a sine wave is given by y = A * sin(B * (t - C)), where:
A represents the amplitude of the wave,
B represents the frequency (in radians per unit of independent variable),
C represents the phase shift (horizontal shift).
In our given equation, y = 25sin(120t - 4x), the coefficient in front of 't' (120) represents the frequency of the wave.
Frequency = B = 120 (in radians per unit of independent variable)
To determine the period, we need to know the relationship between frequency and period. In a sine wave, the period (T) is given by:
Period (T) = 2π / Frequency (B)
For our equation,
Period (T) = 2π / 120
Now, let's calculate the value of the period.
Period (T) = 2π / 120
= π / 60
So, the period of the given wave motion is π/60, and the frequency is 120 (in radians per unit of independent variable).