# Shockwave destroying a house

1. Aug 8, 2009

Shockwave destroying a house [Solved]

1. The problem statement, all variables and given/known data
A 1-megaton nuclear explosion produces a shock wave whose amplitude, measured as excess air pressure above normal atmospheric pressure, is 1.4x10^5 Pa at a distance of 1.3km from the explosion. An excess pressure of 3.5x10^4 Pa will destroy a typical wood-frame house. At what distance from the explosion will such houses be destroyed? Assume the wavefront is spherical.

2. Relevant equations
$$I=\frac{P}{A}$$
$$A=4\pi R^2$$

3. The attempt at a solution
I just treated the excess air pressure as "intensity". Assuming the force drops off as the inverse square of distance.
$$P=IA=1.4\times10^5\times 4 \pi \times 1.3^2=2973203.3$$
$$P=I_1 A_1$$
$$2973203.3=3.5\times 10^4 \times 4\pi R^2$$
$$R^2=6.76km^2$$
$$R=2.6km$$
in the book the answer gives 5.6km, looks like i am out by a factor of 2, not sure how though.

Last edited: Aug 9, 2009
2. Aug 8, 2009

### ideasrule

But amplitude is not intensity; rather, intensity is proportional to the square of amplitude. Think about the simplest oscilliating system: a spring. The energy stored is kA^2, where A is amplitude. Since intensity is simply energy per time divided by area, and since the shockwave is an oscillation, intensity scales as the square of the amplitude as well.

3. Aug 9, 2009