Shortest path is not always the fastest!

The phrase "shortest path may not be the fastest path" is not unknown to anyone. It is very easy to find  analogies for this in real world like traveling from Clementi Avenue 4 to 12A Kent Ridge Road has two main roads and the shortest takes the longer time. But what I am going to put forward is an example from physical world, again not unknown, but even i was unaware before coming here. 

An easier of the scenario would be to imagine 2 ships some 100s of distance apart. If we have to send sound waves, what would be the faster way to do it ? To send it in air or in water ? Well the answer is sound travels almost 5 times faster in air than water.

Imagine a second scenario in which a hydrophone (a device that can sense pressure waves and hence sound) submerged 10 meter deep into water, 100 meters away from an acoustic pinger (a device that produces sound waves of specific frequency at certain frequency). The sound waves reaching the hydrophone have infinite number of paths from pinger to hydrophone like a direct arrival, reflection from surface of ocean to arrive at hydrophone or reflection from sea bed to arrive at hydrophone. 

Intuitively it seems that direct arrival would be fastest but that is not necessary. It can be possible that a reflection from surface or bed can be faster. And the reason is the fact that sound speed varies with temperature, salinity and pressure. the plot below explains the variation of above factors with depth. 

Analytically the variation of speed of sound with temperature, salinity and depth is approximately

Temperature 1°C = 4.0 m/s
Salinity 1PSU = 1.4 m/s
Depth (pressure) 1km = 17 m/s

if these three are taken into account together, as they exist in nature, then speed of sound varies as

The sound speed increases with salinity and pressure which also increase with depth, but temperature decreases with depth till some depth, and speed of sound is more for hotter water. So near the surface sound moves faster than that of some depth. Later the decreases of temperature is over come by increasing pressure and salinity and finally sound speed keeps on increasing. 

Thanks to depletion of Amplitude of reflected wave, we can distinguish between direct arrival and surface reflections, even if direct arrival come later.