A wave on a string is described by D (x,t) = (2.00 cm) ✕ sin [(12.57 rad/m)x ─ (638 rad/s) t], where x is in m and t in s. The linear density of the string is 5.00 g/m. What arec. The maximum speed of a point on the string?

The vertical displacement of a wave moving along the x-axis is given by$y\left(x,t\right)=\left(0.045\mathrm{m}\right)\cos \left(\left(3.4\mathrm{Hz}\right)t-\left(4.5{\mathrm{m}}^{-1}\right)x\right)$. What is the wave speed and in what direction is it traveling?

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x, t)=2.30mm cos[(16.98 rad/m^)x+(742 rad/s)t]. Being more practical, you measure the rope to have a length of 1.35 m and a mass of 0.00338 kg. You are then asked to determine the following: (d) wave speed; (e) direction the wave is traveling;

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x, t)=2.30mm cos[(16.98 rad/m^)x+(742 rad/s)t]. Being more practical, you measure the rope to have a length of 1.35 m and a mass of 0.00338 kg. You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength; (d) wave speed; (e) direction the wave is traveling; (f) tension in the rope; (g) average power transmitted by the wave.

A sound wave is described by D (y,t) = (0.0200 mm) ✕ sin [(8.96 rad/m)y + (3140 rad/s)t + π/4 rad], where y is in m and t is in s.b. Along which axis is the air oscillating?

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

Show that the displacement D(x,t) = cx² + dt², where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.

Show that the displacement D(x,t) = ln(ax + bt), where a and b are constants, is a solution to the wave equation. Then find an expression in terms of a and b for the wave speed.