18. Waves & Sound

A wave traveling to the right has an Amplitude of 15 cm, wavelength of 40 cm, and oscillates 8 times per second. At t = 0, the displacement of a particle at x = 0 along this wave is +15 cm. Write the wave function, including the phase constant, using a sine function.

FIGURE P16.45 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left. Write the displacement equation for this wave.

A wave on a string is described by $D(x,t)=\left(2.00\text{cm}\right)\times \sin \left[\right(12.57\text{rad/m})x-(638\text{rad/s}\left)t\right]$, where $x$ is in $m$ and $t$ in $s$. The linear density of the string is $5.00\text{ g/m}$. What are The maximum speed of a point on the string?

A 572-Hz longitudinal wave in air has a speed of 345 m/s. At a particular instant, what is the phase difference (in degrees) between two points 4.4 cm apart?

A 572-Hz longitudinal wave in air has a speed of 345 m/s. How much time is required for the phase to change by 90° at a given point in space?

Given an oscillation described by $x=A\cos (\omega t+\varphi )$, where the phase constant $\varphi$ can range from $-180°$ to $180°$, which of the following values for $\varphi$ is correct if the oscillation starts at its maximum positive displacement at $t=0$?

In the context of simple harmonic motion described by the equation $x=Acos\left(\phi \right)$, what does the phase constant $\phi$ represent, given that $-180°\le \phi \le 180°$?

In the context of simple harmonic motion, what does the phase constant represent in the equation $x=Acos(\omega t+\phi )$?