Question

calculate the percent error made over one mile of distance by the 5 sec.rule for estimating the distance from a lighting strike if the temperature (a) 300 c (b) 100 c

Answer 1

Answer on Question #49419, Physics, Acoustics

Calculate the percent error made over one mile of distance by the 5 sec. rule for estimating the distance from a lighting strike if the temperature (a) $30{}^{\circ}\mathrm{C}$ (b) $10{}^{\circ}\mathrm{C}$

Solution:

The "5 second rule" says that for every 5 seconds between seeing a lightning strike and hearing the associated sound, the lightning is 1 mile distant. We assume that there are 5 seconds between seeing the lightning and hearing the sound.

(a) At $30{}^{\circ}\mathrm{C}$, the speed of sound is $[331 + 0.60(30)]\mathrm{m/s} = 349\mathrm{m/s}$.

The actual distance to the lightning is therefore

$$d = vt = (349\mathrm{m} \cdot s)(5s) = 1745\mathrm{m}.$$

A mile is 1610 m.

$$\% \text{error} = \frac{1745 - 1610}{1745} * 100 = 7.7\% \approx 8\%$$

(b) At $10{}^{\circ}\mathrm{C}$, the speed of sound is $[331 + 0.60(10)]\mathrm{m/s} = 337\mathrm{m/s}$.

The actual distance to the lightning is therefore

$$d = vt = (337\mathrm{m} \cdot s)(5s) = 1685\mathrm{m}.$$

A mile is 1610 m.

$$\% \text{error} = \frac{1685 - 1610}{1685} * 100 = 4.45\% \approx 4.5\%$$

Answer: a) $8\%$; b) $4.5\%$.

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