Chapter 27, Problem 65A

Stephen uses his cell phone to talk to Fiona, who is reading downstairs, 12 meters away. The phone signal leaves Stephen’s phone, travels 6.0 km to a cell tower, and then is immediately sent to Fiona’s phone. When Stephen speaks, how long does the signal take to get from his phone to Fiona’s phone? How does this time compare with the time it would take for the sound to travel to Fiona if Stephen instead just yelled downstairs?

To determine

To Calculate: The time taken by the signal to reach from person S’s phone to person F’s phone via cell tower and time for the sound to travel to person F directly.

Answer to Problem 65A

The cell phone signal is 875 times faster.

Explanation of Solution

Given info:

The distance between the cell phone and cell tower is 6 km

Distance between the cell phone and person F is 12 m

Formula used:

  $t=\frac{d}{v}$

Here, t is the time, d is the distance and v is the speed.

Calculation:

Time taken by the cell phone signals:

  $t=\frac{d}{v}$

Signal goes from phone to tower and then tower to phone. So, distance travelled will be doubled.

Here, distance from phone to tower is

  $6\text{km}=\text{6000}\text{m}$

  $\text{Then}$

  $\text{d}=\text{2}\times \text{6000}$

  $=\text{12000}\text{m}$

And the speed of light is $c=3\times {10}^8\text{m/s}$

Then,

  $\begin{array}{l}{t}_{signal}=\frac{d}{c}\\ =\frac{12000}{3\times {10}^8}\\ =4\times {10}^{-5}\text{s}\end{array}$

Speed of sound =

  $343m/s$

Time taken by the sound,

  $\begin{array}{l}{t}_{sound}=\frac{d}{c}\\ =\frac{\text{12}}{\text{343}}\\ =0.035\mathrm{s}\end{array}$

So,

  $\begin{array}{c}\frac{t_{sound}}{t_{signal}}=\frac{0.035}{4\times {10}^{-5}}\\ =875\end{array}$

Conclusion:

The cell phone signal is 875 times faster.