wave equation

1. The wave equation : y = (0.15).sin[(2pi/16)x - (64pi/16)t]
Hence, the wave no. k = 2(pi)/16
But wave no k = 2.pi/入 where 入 is the wavelength of the wave
hence, 2.pi/入 = 2(pi)/16
入 = 16 m

The t = 0, y = (0.15)sin[(2pi/16)x]
Maxima occur when sin[(2.pi/16)x] = 1
The 1st max occurs when [(2pi/16)x] = pi/2, i.e. x = 4m
The 2nd max occurs when [(2.pi/16)x] = 2pi + pi/2
i.e. (pi)x/8 = 5(pi)/2
x = 20 m

2. Wavelength 入 = 330/400 m
Hence, wave no k = 2.pi/入 = (2.pi)(400/330) m^-1
Angular frequency w = (2.pi).(400) s^-1 = 800(pi) s^-1

The wave equation: y = (0.02).sin(kx - wt)
i.e. y = (0.02).sin[(800pi/330)x - (800pi)t]
y = (0.02).sin[(800pi).(x/330 - t)]

1. y = 0.15 sin (pi/8 x - pi/4 t)
angular frequency = 2pi/T = pi/8
T = 16m
x-coordinate of second maximum = T + (1/4)T = 16 + 4 = 20m

2. angular frequency ω = 2pi f = 880 pi
v = fλ => λ = 330/440 = 0.75 m
angular wave number k = 2pi/λ = 2pi/0.75 = 8pi/3

y = A sin (kx - ωt) + φ, negative sign to denote the +x-axis wave oscillation & phase change φ = 0 in this case.
hence y = 0.02 sin (8pi/3 x - 880pi t) = 0.02 sin (880pi (x/330 - t))