To find the amplitude of the right moving wave and the left moving wave, we need to consider the equation of the standing wave:
y(x,t) = (3 mm)sin(x/2 m)cos(100 rad/s*t)
Since the equation is in the form of the product of sine and cosine, we can write it as:
y(x,t) = (3 mm)[(1/2)(sin[(x/2 m) + 100 rad/s*t]) + (1/2)(sin[(x/2 m) - 100 rad/s*t])]
Now, we can see that the amplitude of the right moving wave is (3 mm)/2 = 1.5 mm, and the amplitude of the left moving wave is (3 mm)/2 = 1.5 mm.
To determine the wavelength of the right moving wave and left moving wave, we need to find the distance between two consecutive maxima or minima for each wave.
For the right moving wave, the wavelength is given as:
λ = 2π/k,
where k = x/2 m.
Therefore, the wavelength of the right moving wave is 2π/[(x/2 m)] = 4π/x.
Similarly, for the left moving wave, the wavelength is also given as:
λ = 2π/k,
where k = -(x/2 m).
Therefore, the wavelength of the left moving wave is 2π/[-(x/2 m)] = 4π/[-(x/2)] = -4π/x.
Note that the wavelength can be positive or negative, but for the purpose of this calculation, we take the absolute value.
Finally, to find the velocity of the right moving wave and left moving wave, we use the formula:
v = fλ,
where v is the velocity, f is the frequency (in this case, it is 100 Hz), and λ is the wavelength.
For the right moving wave, the velocity (v1) is given by:
v1 = (100 Hz) * (4π/x) = (400π/x) m/s.
For the left moving wave, the velocity (v2) is given by:
v2 = (100 Hz) * (-4π/x) = (-400π/x) m/s.
Thus, the velocity of the right moving wave is (400π/x) m/s, and the velocity of the left moving wave is (-400π/x) m/s.