Question

The splash is heard $2.05s$ after the stone is dropped into a well of depth $19.6m$. The velocity of sound is?

• A. $342$ $m{s}^{-1}$
• B. $372$ $m{s}^{-1}$
• C. $392$ $m{s}^{-1}$
• D. $352$ $m{s}^{-1}$

Answer 1

The correct option is C $392$ $m{s}^{-1}$

If we use$g=9.8m/s^2$ for the acceleration of gravity, and assume that there are no frictional forces to slow the stone down as it falls, then using the second equation of motion $h=\frac{1}{2}{gt}^2$ gives $t=2s$t=2sas the time at which the stone hits the water (we’re also ignoring precisely what point the stone is at $19.6m$19.6m above the water).

Assuming that the sound waves are emitted precisely at the moment of contact between the stone and the water, and that there is no physiological time lag in “hearing” the sound (e.g., time for auditory nerve conduction), then this means that the sound waves travel $19.6m$19.6m in $t=(2.05-2)s$0.05s, so that their average speed is $\frac{19.6}{0.05}=392m/s$