Two neighbors communicate with a homemade string phone (see figure below). The s

Question

Two neighbors communicate with a homemade string phone (see figure below). The simple phone consists of two ends of a string (total mass of 13 g) attached to the bottom of two paper cups. The string is stretched between the two homes at a tension of 22 N over the distance of 37 m.

(a) How long does it take communication to travel on the string from one home to the other?

(b) How long would it take to communicate by yelling out the window?

(c) How long would it take to communicate over cell phones if the nearest cell tower is 5.1 km away? (Consider only the propagation time of the radio waves and assume that the call is already connected)

Please show all work!

Explanation / Answer

mass per unit length=13/37=0.351 gram/m

so speed of wave=sqrt(tension/mass per unit length)=250.23 m/s

a)time=distance/speed=0.1478 seconds

b)speed of sound=343 m/s

so yeling to be heard,time taken=37/343=0.1078 sec

c)speed of radio wave=3*10^8 m/s

so time taken=2*(5.1*1000)/(3*10^8)=3.4*10^(-5) seconds

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