Chapter 12, Problem 2TS

From far away you watch a woman driving nails into her front porch at a regular rate of one stroke per second. You hear the sound of the blows exactly synchronized with the blows you see. And then you hear one more blow after you see her cease hammering. How far away is she?

To determine

The distance where the woman is standing.

Answer to Problem 2TS

The distance where the woman is standing is $340\text{m}$

Explanation of Solution

Given Info: The number of strokes is $1$ and the time $1\text{}\sec$.

Write the expression for the frequency.

$F=\frac{n}{t}$

Here,

$n$ is the number of strokes

$t$ is the time taken

Substitute $1\text{}\sec$ for $t$ and, $1$ for $n$ in the above expression to get $F$.

$\begin{array}{c}F=\frac{1}{1\sec }\\ =1\text{Hz}\end{array}$

Write the expression for period.

$T=\frac{1}{F}$

Substitute $1\text{Hz}$ for $F$ in the above equation to calculate $T$.

$\begin{array}{c}T=\frac{1}{1\text{Hz}}\\ =1\sec \end{array}$

Write the expression for distance, at which the woman is standing.

$d=v.t$

Here,

$v$ is the speed of the sound

$t$ is the period.

Substitute $1\sec$ for $T$ and $340\text{m/}\sec$ for $v$ in the above expression to get $d$.

$\begin{array}{c}d=340\text{m}/\sec \times 1\sec \\ =340\text{m}\end{array}$

Conclusion:

Therefore, the distance where the woman is standing is $340\text{m}$.