Chapter 22, Problem 16P

To determine

The person who listens to the voice-first and by how much time faster they listen.

Answer to Problem 16P

The answer is the person at radio hears the voice $0.1357s$ sooner.

Explanation of Solution

Given data:

Distance, $d_{radio}=3000km,d_{sound}=50m$

Speed of light, $c=3\times {10}^{8}m/s$

Speed of the sound, $v_{\text{sound}}=343\text{m/s}$

Formula used:

It is known that:

  $\Delta t=t_{radio}-t_{sound}=\left(\frac{d_{radio}}{c}\right)-\left(\frac{d_{sound}}{v_{sound}}\right)$

Where,

  $v_{\text{sound}}$ is the speed of sound.

  $d_{radio}\&d_{sound}$ is the distance.

  $c$ is speed of the light.

  $\Delta t$ is change in time.

Calculation:

Substitute the given data into the formula $\Delta t=\left(\frac{d_{radio}}{c}\right)-\left(\frac{d_{sound}}{v_{sound}}\right)$

  $\Delta t=\left(\frac{3\times {10}^{6}m}{3.00\times {10}^{8}m/s}\right)-\left(\frac{50m}{343m/s}\right)=0.01-0.145772594=0.1357s$

Conclusion: The person at the radio hears the voice $0.1357s$ sooner.