Question

You see your friend 100 m away down the street. If you yell back and forth, your conversation will be affected by the speed of sound, which is 340 m/s. If, instead, you use your cell phone to call her on her cell phone, the conversation is relayed via a communications satellite that is 36000 km above you. What is the delay between a sound leaving your mouth and its arrival at your friend’s ear if (a) you yell, or (b) you use your cell phone? (c) How far would you have to be from your friend for the delays to be equal?

Answer 1

(a) 0.29 s

If you yell, your voice will reach your friend by travelling as a sound wave through the air.

The speed of sound in air is

v = 340 m/s

while the distance to be covered is

d = 100 m

So, the time taken is

`t=(d)/(v)=(100 m)/(340 m/s)=0.29 s`

(b) 0.24 s

In this case, the voice is transmitted as a radio wave (electromagnetic wave) to the satellite and then back.

The speed of electromagnetic waves is the speed of light:

`c=3\cdot 10^8 m/s`

while the distance the wave has to cover is twice the distance between the ground and the satellite:

`d=2 \cdot 36000 km=72000 km=7.2 \cdot 10^7 m`

So, the time taken is

`t=(d)/(c)=(7.2\cdot 10^7 m)/(3\cdot 10^8 m/s)=0.24 s`

(c) 81.6 m

In order for the two delays to be equal, the distance between you and your friend (d') must satisfy the equation

`(d')/(v)=(d)/(c)`

where on the left is the time taken by the sound to travel through the air, while on the right is the time taken by the radio wave to travel back and forth from the satellite.

Solving the equation for d',

`d'=v(d)/(c)=(340 m/s)(7.2\cdot 10^7 m)/(3\cdot 10^8 m/s)=81.6 m`