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Find the equation of wave

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The linear mass density of a nonuniform wire under constant tension decreases gradually along the wire so that an incident wave is transmitted without reflection. The wire is uniform for $-\infty < x < 0$. In this region, a transverse wave has the form $$y(x, t) = 0.003 \cos (25x — 50t)$$ where $y$ and $x$ are in meters and $t$ is in seconds. In the region $0 < x < 20$ the linéar mass density decreases gradually from $\mu$ to $\frac14 \mu$. For $20 < x < +\infty$ the linear mass density is $\frac14 \mu$. Then prove that for $x > 20$ the wave equation is $$ y(x,t) = 0.0042 \cos (12.5 x — 50 t)$$

asked May 15 in Physics Problems by koolman (4,286 points)
edited May 15 by sammy gerbil
Good so far. What about amplitude? There is no reflection because the change in mass density is continuous. Therefore the power transmitted by the wave must be the same in both regions $x<0$ and $x>20$. See http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/powstr.html.

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