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 $\lambda$. What is the amplitude of the motion at the points located at (i) $x=\lambda /2$, (ii) $x=\lambda /4$, and (iii) $x=\lambda /8$, from the left-hand end of the string?

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.

One string of a certain musical instrument is 75.0 cm long and has a mass of 8.75 g. It is being played in a room where the speed of sound is 344 m/s. (a) To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.765 m? (Assume that the break-ing stress of the wire is very large and isn't exceeded.) (b) What frequency sound does this string produce in its fundamental mode of vibration?

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 $\(\lambda\)$. How much time does it take the string to go from its largest upward displacement to its largest downward displacement at the 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.