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?

FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string?

One cue your hearing system uses to localize a sound (i.e., to tell where a sound is coming from) is the slight difference in the arrival times of the sound at your ears. Your ears are spaced approximately 20 cm apart. Consider a sound source 5.0 m from the center of your head along a line 45° to your right. What is the difference in arrival times? Give your answer in microseconds. Hint: You are looking for the difference between two numbers that are nearly the same. What does this near equality imply about the necessary precision during intermediate stages of the calculation?

A 20.0-cm-long, 10.0-cm-diameter cylinder with a piston at one end contains 1.34 kg of an unknown liquid. Using the piston to compress the length of the liquid by 1.00 mm increases the pressure by 41.0 atm. What is the speed of sound in the liquid?

A string that is under 50.0 N of tension has linear density 5.0 g/m. A sinusoidal wave with amplitude 3.0 cm and wavelength 2.0 m travels along the string. What is the maximum speed of a particle on the string?

The string in FIGURE P16.59 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string.

A sound wave is described by $D(y,t)=\left(0.0200\text{mm}\right)\times \sin \left[\right(8.96\text{rad/m})y+(3140\text{rad/s})t+\pi /4\text{rad}]$, where $y$ is in $m$ and $t$ is in $s$. Along which axis is the air oscillating?