In: Physics
A mechanical wave is given by the equation: y(x,t) = 0.5 cos (62.8x – 15.7t) , Find: (1) Amplitude, frequency, wavelength? (2) The velocity of the wave? (3) The maximum velocity of the vibrations? (4) Write down the equation in the opposite direction?
Solution;
The given equation is
The above equation can be re-written as
......................................(1)
The general equation of the harmonic wave travelling in +X is given by,
...................(2)
where is initial phase. Comparing (1) & (2), we have
(1) Amplitude
Wavelength
Velocity
frequency
(2) The velocity of the wave is
(3)
The angular speed
The maximum velocity
(4) The equation of the wave travelling in the opposite direction is given by,