18. Waves & Sound

A horizontal string tied at both ends is vibrating in its fundamental mode. The traveling waves have speed $v$, frequency $f$, amplitude $A$, and wavelength $\lambda$. Calculate the maximum transverse velocity and maximum transverse acceleration of points located at (i) $x = λ/2$, (ii) $x = λ/4$, and (iii) $x = λ/8$, from the left-hand end of the string.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin[(32.5\text{ rad/m})x]\sin[(754\text{rad/s})t]$. For the two traveling waves that make up this standing wave, find the wave speed.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin[(32.5\text{ rad/m})x]\sin[(754\text{rad/s})t]$. For the two traveling waves that make up this standing wave, find the frequency.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin[(32.5\text{ rad/m})x]\sin[(754\text{rad/s})t]$. For the two traveling waves that make up this standing wave, find the wavelength.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin \left[\right(32.5\text{ rad/m}\left)x\right]\sin \left[\right(754\text{rad/s}\left)t\right]$. For the two traveling waves that make up this standing wave, find the amplitude.

CALC. A thin, taut string tied at both ends and oscillating in its third harmonic has its shape described by the equation $y(x,t)=\left(5.60\text{ cm}\right)\sin \left[\right(0.0340\text{ rad/cm}\left)x\right]\sin \left[\right(50.0\text{ rad/s}\left)t\right]$, where the origin is at the left end of the string, the $x$-axis is along the string, and the $y$-axis is perpendicular to the string. Draw a sketch that shows the standing-wave pattern.

The fundamental frequency of a pipe that is open at both ends is 524 Hz. the frequency of the new fundamental.