Final answer:
A sinusoidal transverse wave traveling in the negative x-direction on a string can be described by a wave function. It is characterized by simple harmonic motion of points on the string and the formation of a standing wave when combined with a wave moving in the opposite direction. The wave function and properties are affected by the tension and linear mass density of the string.
Step-by-step explanation:
A sinusoidal transverse wave traveling on a string in the negative direction of an x-axis can be modeled by a wave function. Such a wave is characterized by points on the string oscillating in simple harmonic motion, up and down in the y-direction, while the wave itself travels along the string. When two sinusoidal waves moving in opposite directions combine on a string, they can form a standing wave, which appears motionless in the x-direction and is identifiable by its nodes and antinodes.
The speed of a wave on a taut string is determined by the tension and the linear mass density of the string. The linear mass density is important as it affects both the wave speed and the energy transmitted by the wave. The wave equation for a sinusoidal wave moving in the negative x-direction would include a negative sign in front of the wave number multiplied by x in the argument of the sine or cosine function, to indicate the negative direction of movement.