Chapter 12, Problem 7P

(a)

To determine

To Calculate: The percentage error of the given temperature.

Answer to Problem 7P

The percentage error for the distance is $8\%$ .

Explanation of Solution

Given:

Temperature, $T=30°\text{C}$

Formula used:

The speed is calculated as,

  $v=\left(331+0.61T\right)\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.$

Where, T is the temperature in degree Celsius.

The % error formula is,

  $\%\text{error}=\frac{\text{change}\text{in}\text{value}}{\text{original}\text{value}}\times 100$

Calculation:

According to 5-second rule, for each 5-second between seeing a lightning strike and associated Sound. The lightning is one mile distant.

Now, consider a fact that there are 5 seconds between seeing the lighting and the associated sound. So, the speed of the light is,

  $\begin{array}{l}v=\left(331+0.61T\right)\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.\\ =\left(331+0.61\times \left(30°\text{C}\right)\right)\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.\\ =349\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.\end{array}$

The distance to the lightning is,

  $\begin{array}{l}d=v\times t\\ =\left(349\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.\right)\times \left(5\mathrm{s}\right)\\ =1745\text{m}\end{array}$

One mile is equal to the $1610\text{m}$

Now, the percentage error of the given temperature is,

  $\begin{array}{l}\%\text{error}=\frac{\text{change}\text{in}\text{value}}{\text{original}\text{value}}\times 100\\ =\frac{1745\text{m}-1610\text{m}}{1745\text{m}}=8\%\end{array}$

Conclusion:

The percentage error is $8\%$ .

(b)

To determine

To Calculate: The percentage error of the given temperature.

Answer to Problem 7P

The percentage error for the distance is $4\%$ .

Explanation of Solution

Given:

Temperature, $T=10°\text{C}$

Formula used:

The speed is calculated as,

  $v=\left(331+0.61T\right)\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.$

Where,

T is the temperature in degree Celsius.

The % error formula is,

  $\text{\%}\text{error}\text{=}\frac{\text{change}\text{in}\text{value}}{\text{original}\text{value}}\times 100$

Calculation:

According to 5-second rule, for each 5-second between seeing a lightning strike and associated Sound. The lightning is one mile distant.

Now, consider a fact that there are 5 seconds between seeing the lighting and the associated sound. So, the speed of the light is,

  $\begin{array}{l}v=\left(331+0.61T\right)\\ =\left(331+0.61\times \left(10°\text{C}\right)\right)\\ =337\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.\end{array}$

The distance to the lightning is,

  $\begin{array}{l}d=v\times t\\ =\left(337\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.\right)\times \left(5\sec \right)\\ =1685\text{m}\end{array}$

One mile is equal to the $1610\text{m}$

Now, the percentage error of the given temperature is,

  $\begin{array}{l}\text{\%}\text{error}\text{=}\frac{\text{change}\text{in}\text{value}}{\text{original}\text{value}}\times 100\\ =\frac{\text{1685m}-\text{1610m}}{\text{1685m}}=4\%\end{array}$

Conclusion:

The error percentage is $4\%$