Wave Function

The figure shows the vibration graph of object A undergoing simple harmonic motion: displacement $x$ (in cm) versus time $t$ (in units of 0.1 s). The curve is a sine that leaves the origin rising, reaches $+10$ cm at $t = 0.1$ s, returns to zero at $t = 0.2$ s, reaches $-10$ cm at $t = 0.3$ s, and completes one full cycle at $t = 0.4$ s.

A long horizontal rope is fixed at one end while the other end is driven by a rod that continuously oscillates up and down in simple harmonic motion, producing a simple harmonic wave on the rope. The distance between the highest and lowest points of the rope's transverse motion is $0.50$ cm, the rod oscillates 120 times each second, and the wave speed on the rope is $19$ m/s.

A mechanical transverse wave propagating along the $y$-axis is described by $x = 6.0 \times 10^{-2}\cos(4.0\pi t - 2.0\pi y)$ m, where $x$ is the transverse displacement (in m), $y$ the position along the axis (in m), and $t$ the time (in s).

A simple harmonic wave travels along a rope. A point on the rope takes $0.17$ s to move from the position of maximum displacement back to its equilibrium position.

A transverse wave travels along a string in the $+y$ direction. There are 6000 wavelengths in each meter of the string, the period is $0.20$ s, and the amplitude is $3.0$ cm.

A transverse wave traveling along a long string is described by

A wave propagates in the negative $y$ direction with amplitude $1.0\times10^{-2}$ m, frequency 550 Hz, and wave speed 330 m/s.

At a certain instant, a simple harmonic wave of amplitude $A = 0.2$ m, period $T$, and wavelength $\lambda$ travels in the $+y$ direction. At this instant the transverse displacements are: a crest $x = +0.2$ m at point $O$ ($y = 0$), zero at $a$ ($y = \lambda/4$), a trough $x = -0.2$ m at $b$ ($y = \lambda/2$), zero at $c$ ($y = 3\lambda/4$), and a crest at $d$ ($y = \lambda$). Take $t = 0$ at this instant.

A spring oscillator moves along the $x$ axis. At $t = 0$ its position is $x_0 = 3$ cm and it is moving in the $+x$ direction with speed $v_0 = 6\pi$ cm/s. Its oscillation frequency is $ u = 1$ Hz.