I was recently driving back to Northborough from Rochester, NY after the holidays when a thought hit me. After rubbing the bruise the thought gave me I began to think. Say one person in a car crosses the MA border from NY on I-90 and beeps his/her horn. The next person closest to them on I-90 then beeps there horn in some sort of automotive relay race. This continues for however long it takes until â€œThe Beepâ€ reaches Boston. Now stemming from this thought I had several quandries; 1: How long would it take â€œThe Beepâ€ to reach Boston from the Ma/NY border? 2: How many cars would it take to necsesitate â€œThe Beep”? and finally 3: Would the fact that the cars are all moving towards boston speed up â€œThe Beepâ€ in any measurable amount?
Hope you had a good holiday shaun and i canâ€™t wait to hear your answer!
Comment by Kurt â€” 12/30/2004 @ 1:42 pm
I had to call in the big guns on this one. Many thanks to Jen (of Shamus and Jen) for the mathematical support.
Here are the FACTS:
1. The Mass Pike is 138 miles long from the NY border to its end in Boston.
2. Sound travels at 740 miles per hour in 30 degree air.
3. The cars are moving at an average of 70 miles per hour.
4. At 70 MPH, the safe distance between you and the next car is 7 times the length of your car.
5. The average car is 9 feet in length.
6. There are 5280 feet in a mile.
Here are the ASSUMPTIONS:
1. The location of the horn is in the back of the FIRST car.
2. The number of cars is fixed (moving area of interest).
Here is the MATH:
5280 ft * 138 miles = 728640 ft.
10120 cars to get through.
(9 *7) = 63 ft between cars.
63 ft / 5280 = 0.011932 miles between cars.
740 MPH (speed of sound) – 70 MPH (speed of car) = 670 MPH.
1 hour / 670 MPH * 0.011932 = 0.000018 hrs * 3600 seconds in an hour = 0.064111 seconds.
0.085 seconds to get sound from back of car to front.
So the final equation is:
(10120 cars) * (0.085 seconds) + (10120) * (0.064111 seconds) = 1509 seconds.
1509 seconds = 25.15 minutes.
So, to answer your questions:
1. It would take 25.15 minutes for “The Beep” to get to Boston.
2. The number of cars needed to actualize “The Beep” would be 10120.
3. The speed the cars are traveling does NOT increase the speed of the beep. Rather the opposite actually.