One way to monitor global warming is to measure the average temperature of the o

Question

One way to monitor global warming is to measure the average temperature of the ocean. Researchers are doing this by measuring the time it takes sound pulses to travel underwater over large distances. At a depth of 1000 m, where ocean temperatures hold steady near 4C, the average sound speed is 1480m/s. It's known from laboratory measurements that the sound speed increases 4.0m/s for every 1.0C increase in temperature. In one experiment, where sounds generated near California are detected in the South Pacific, the sound waves travel 7500 km .

If the smallest time change that can be reliably detected is 1.0 s, what is the smallest change in average temperature that can be measured?

Explanation / Answer

Given

that the separation between two points is d = 7500 km

Average speed of the sound is v = 1480 m/s

The time taken by the sound to travel the distance is given by

t = d / v

= 7500 km / 1480 m/s

= 7500x103 m / 1480 m/s

= 5067.5 s

But the change in time is gievn by 1.0 s. Then the new time is given by

t' = 5067.5 s

Then the new speed of sound is

v' = d / t'

= 7500*103 m / 5067.5 s

= 1480.01m/s

From given data speed increases 4.0 m/s for every 1.0 oC

So for 0.01m/s(1480.01-1480) the increase in temperature is

(1oC / 4.0 m/s)(0.01 m/s) = 2.5*10^-3 oC

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