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 4 degrees C, the average sound speed is 1480 m/s. It's known from laboratory measurements that the sound speed increases 4.0 m/s for every 1.0 degree C increase in temperature. In one experiment, where sounds generated near California are detected in the South Pacific, the sound waves travel 8300 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?
Express your answer using two significant figures.
t = _________degree C

Explanation / Answer

Given that the separation between two points is d = 8300 km Average speed of the sound is v = 1480 m/s ------------------------------------------------------------------------ time taken to travel the distance by sound is           t = d / v             = 8300 km / 1480 m/s             = 8300x103 m / 1480 m/s             =5608.1 s The change in time is 1.0s so the new time is           t' = 5607.1 s Then the speed of sound is              v' = d / t'                     = 8300x103 m / 5607.1s                  = 1480.26 m/s From given data speed increases 4.0 m/s for every 1.0 oC So for 0.26 m/s the increase in temperature is                 (1oC / 4.0 m/s)(0.26 m/s) = 0.065 oC                                   = 1480.26 m/s From given data speed increases 4.0 m/s for every 1.0 oC So for 0.26 m/s the increase in temperature is                 (1oC / 4.0 m/s)(0.26 m/s) = 0.065 oC

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---