18. Waves & Sound

Write the equation for the wave in Problem 29 traveling to the right, if its amplitude is 0.020 cm, and D = - 0.020 cm, at t = 0 and x = 0.

A transverse wave on a cord is given by D(x,t) = 0.12 sin (3.0x - 15.0t), where D and x are in meters and t is in seconds. At t = 0.20s, what are the displacement, velocity, and acceleration of a point on the cord where x = 0.60 m?

A transverse wave with a frequency of 220 Hz and a wavelength of 10.0 cm is traveling along a cord. The maximum speed of particles on the cord is 0.10 the wave speed. What is the amplitude of the wave?

A transverse wave pulse travels to the right along a string with a speed v = 2.0 m/s. At the shape of the pulse is given by the function D = 0.45 cos (2.6x + 1.2), where D and x are in meters. Determine a formula for the wave pulse at any time t assuming there are no frictional losses.

Figure 15–44 shows the wave shape at two instants of time for a sinusoidal wave traveling to the right. What is the mathematical representation of this wave?

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.

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 2.0-m-long string vibrates at its second-harmonic frequency with a maximum amplitude of 2.0 cm. One end of the string is at x = 0 cm. Find the oscillation amplitude at x = 10, 20, 30, 40, and 50 cm.

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?

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?

FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.