Discussion
The wave equation \( z_{tt} = c^{2} z_{xx} \) is of which type?
Answer: D
Rearranged as \( z_{tt} - c^{2}z_{xx} = 0 \) we have \( A = 1 \), \( B = 0 \), \( C = -c^{2} \), so
\[ B^{2} - 4AC \;=\; 4c^{2} \;>\; 0 \]
for any non-zero \( c \), the hyperbolic case. Hyperbolic equations carry disturbances along characteristics at finite speed, which is what makes a wave a wave
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