1. Read (or listen) to this story about the recent European clock slowdown: http

Question

1. Read (or listen) to this story about the recent European clock slowdown: http://n.pr/2p1X893

(a) Assume the six-minute delay experienced by clocks in Europe was accumulated between January 15 and March 7, 2018. Determine as precisely as possible the average frequency of the European power grid during this time. Show your work.

(b) Suppose the frequency of the United States power grid increased by 1% relative to its standard value. (If you don’t know the standard frequency of the US power grid, look it up!) How long would it take (measured in hours) for clocks to advance by 15 minutes?

(50 times per second, this device is going to see a voltage peak and a voltage minimum. And so it uses this oscillation in order to keep track of time.But over the last month and a half, that actually adds up to quite a bit. about 6 minutes or about 344 seconds.)

Explanation / Answer

Part (a):

January 15 to March 7: that is 21 days, which is

number of seconds in 21days = 21x24(hours/day)x60(minute/hour)x60(seconds/minute) = 1814400 seconds

According to http://n.pr/2p1X893, in the explanation how the clock went off, it was said it was off about 1/100 th of the cycle.

Hence:

Time in seconds off by the clock = Total number of seconds in that time period x frequency of the error happening.

Frequency of the error happening is = Frequency of the European grid x off factor (1/100 here)

Given time in seconds off by the clock = 6 minutes = 360 seconds

360 seconds = 1814400 / ( F x 100)

F = 50.4 Hertz

Part (b):

Standard frequency of the US power grid = 60 Hertz

Hence if we increase this by 1% the resultant frequency would be = 60 + 0.6 = 60.6 Hz

Hence using the formula in part (a):

Time in seconds off by the clock = Total number of seconds in that time period x frequency of the error happening.

Given: Time in seconds off by the clock = 15 minutes = 900 seconds.

Hence:

900 = X(days) x 86400(seconds/day) / (100 x 60.6)

X = 63.125 days = 2 months

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.