The equation for the other wave is y₂(x, t) = 0.30 cm sin(3 m⁻¹x + 4 s⁻¹t). The amplitude, wave number, wave speed, and the sign in front of the time variable can be found from the given information.
The equation for one of the waves is y₁(x, t) = 0.30 cm sin(3 m⁻¹x - 4 s⁻¹t). To find the equation for the other wave, we need to reverse the sign in front of the time variable. So, the equation for the other wave is y₂(x, t) = 0.30 cm sin(3 m⁻¹x + 4 s⁻¹t).
(a) The amplitude (ym) is 0.30 cm.
(b) The wave number (k) is 3 m⁻¹.
(c) The wave speed (v) is 100 m/s.
(d) The sign in front of the time variable is + for the second wave equation.
--The given question is incomplete, the complete question is
"Two waves are generated on a string of length 3.0 m to produce a three-loop standing wave with an amplitude of 1.0 cm. The wave speed is 100 m/s. Let the equation for one of the waves be of the form y(x, t) # ym sin(kx " vt). In the equation for the other wave, what are (a) ym, (b) k, (c) v, and (d) the sign in front of v?"--