In this problem, we are going to derive various information related to the frequency of a wave.
A maser is a laser-type device that produces electromagnetic waves with frequencies in the microwave and radio-wave bands of the electromagnetic spectrum. You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another name for one cycle per second.) A clock controlled by a hydrogen maser is off by only 1 s in 100,000 years. (The large number of significant figures given for the frequency simply illustrates the remarkable accuracy to which it has been measured.)
A. What is the time for one cycle of the radio wave? Express your answer to three significant figures and include the appropriate units.
B. How many cycles occur in 4 h? Express your answer using three significant figures.
C. How many cycles would have occurred during the age of the earth, which is estimated to be 4.6×109 years? Express your answer using three significant figures.
D. By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth? Express your answer using three significant figures.
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