Question

Three Students: Samantha, Colton and Elizabeth are standing the same distance from an explosion. Samantha wears a blindfold and hears the explosion only. Fulton wears headphones so will only know when the explosion happens based on sound. Elizabeth will be blindfolded and wearing headphones. She will feel the explosion through the ground. Predict what order the studetns will know that the explosion happened. Explain below. *

Answer 1

The cinematic allows finding that Elizabeth is the first to hear the sound, Samantha is the second person to hear the explosion and Fulton the last, since he has the time in the air plus the transformation time of the sound in the headphones.

When an object explodes, a sound wave of great intensity is produced, this wave propagates through the different media with which it is in contact.

The speed of sound in each medium is given by the expressions

          v = $\sqrt{\frac{B}{\rho } }$

Where B is the volumetric modulus, ρ the density of the medium.

Sound is a wave so its velocity is constant, so we can use the kinematic relationships for uniform motion

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

Some values ​​of interest for the speed of sound are

Medium          speed (m / s)

air                          340  

liquid            order of 1500  

Solids           order of 4000

In this exercise, the three students are at the same distance, so Elizabeth who hears the explosion through the ground ( solid) should be the person who first hears it.

For the other two students the time difference must be small, Samantha hears the explosive that is transmitted in the air.

Fulton uses headphones, so the explosion must excite a bugle that transforms the sound into signals for the headphones and again transforms it into audible signals.

The headphones are next to it. The time of the signal is the time in the air plus the time of the electrical signal, so you should hear the sound after Samatha.

In conclusion using the kinematics we can find that Elizabeth is the first to hear the sound and possibly Samantha is the second person to hear the explosion and Fulton the last since he has the time in the air plus the transformation time.

Learn more about sound here:

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