Energy in Pulses II

Two half-infinite strings are connected at $x=0$, see Fig. 2. The wave speed in the thin string ($x<0$) is 100 m/sec, and in the thick string $(x>0)$ it's 50 m/sec. A pulse is coming from the left; the shape of the pulse at $t=0$ is shown in Fig. 2.

(a)

Sketch the shape of the strings at $t=0.1$ sec.
HINT: The impedance of a string is given by $Z=\tau/c$, where $c$ is the wave speed and $\tau$ is the tension, common to both strings.

(b)

Compute and graph the total energy density at $t=0$ and $t=0.2$ sec.

(c)

Compute the total energy of the incoming pulse. Repeat the calculation for the reflected and transmitted pulses. Verify conservation of energy.

Figure 2: Two half-infinite strings.