Question

While filming an intense action sequence for the next James Bond movie, a controlled explosion detonates 1.3 km away from the actors. If the speed of sound through solid rock is 3000 m/s on average, the actors will feel the explosion before they hear it. How much time will pass between when they feel the explosion and when they hear it?

Answer 1

To solve this problem we must basically resort to the kinematic equations of movement. For which speed is defined as the distance traveled in a given time. Mathematically this can be expressed as

$v = \frac{d}{t}$

Where

d = Distance

t = time

For which clearing the time we will have the expression

$t = \frac{d}{v}$

Since we have two 'fluids' in which the sound travels at different speeds we will have that for the rock the time elapsed to feel the explosion will be:

$t = \frac{1300m}{3000m/s}$

$t = 0.433s$

In the case of the atmosphere -composite of air- the average speed of sound is 343m / s, therefore it will take

$t = \frac{1300m}{343m/s}$

$t = 3.79s$

The total difference between the two times would be

$\Delta t = 3.79s-0.433s$

$\Delta t = 3.357s$

Therefore 3.357s will pass between when they feel the explosion and when they hear it