Forces and Motion

Oscillations and clocks

Teaching Guidance for 14-16 PRACTICAL PHYISCS

Isochronous oscillators, from the pendulum to the precise oscillations of a caesium atoms in an atomic clock, have an obvious practical use in the measurement of time. But there is more to time than making accurate clocks.

The longitude problem

Early navigators could measure latitude (from the altitude of the sun at noon) but they had to rely on ‘dead reckoning’ to find longitude. Between the 15th and 17th centuries there was huge growth in European trade based on shipping. Accurate and reliable navigation at sea became vitally important, because failing to identify a ship's position near land could cause a shipwreck and, with it, the loss of not only cargo but also sailors’ lives. In 1707 the British Parliament passed The Longitude Act, which offered a substantial cash reward to anyone who could demonstrate a way of accurately determining longitude at sea.

A clock offers one way of finding longitude. If sunrise occurs six hours late or early, one has travelled a quarter of the way round the Earth. This means an error of one minute in time makes a navigational error of nearly thirty kilometres at the equator.

In the middle of the eighteenth century, John Harrison solved the longitude problem by making a sea watch (called H4) that would keep good time, despite a ship’s rolling with ocean waves and despite changes in temperature. Between 18 November 1761 and 21 January 1762 Harrison's sea watch was taken on a voyage from England to Jamaica. On arrival, it was tested and found to be in error by only five seconds after its voyage of 81 days. It was possible to test Harrison’s watch against Jamaica time by sighting the Sun at its highest point in the Jamaican sky, which occurs exactly at noon.

The full John Harrison story is told in Dava Sobel’s book Longitude. A brief summary of Harrison’s work on sea-going clocks is freely available online:

Royal Museums Greenwich website

The quartz clock

In the 1930s a new type of clock started to replace the most accurate pendulum clocks as a standard for measuring time. This was the quartz crystal clock. A quartz crystal will vibrate elastically with a natural period of its own, just like a tuning fork. In this case, however, electrical charges constantly build up and die away on its surface in time with the vibrations. It is this effect, the piezoelectric effect, which makes it so easy both to keep the crystal vibrating and to use the vibrations to control the frequency of electrical oscillations in other circuits. It is these electrical oscillations, accurately controlled by the vibrations of the quartz crystal, which drive the hands of the clock or control its display.

Suppose two quartz clocks are adjusted to read exactly the same time and then left to run without adjustment. Comparisons of their time readings at various times later have indicated a difference of no more than 0.0005 s econd per day over a period of a week or so. This suggests that a quartz clock will measure a time interval of 1 day, or 86 400 seconds, to within 0.0005 s econds; an accuracy of better than 1 in 108. This is ten times better timekeeping than the best pendulum clock.

Quartz clocks were initially developed in response to the demand from scientists and engineers for more and more precise time standards, for the purposes of radio communication, navigation, and pure research. It was also in response to this demand that the atomic clock was developed in 1954.

The atomic clock

Atoms can emit and absorb energy only at very sharply defined frequencies. Provided a suitable atom is chosen, they can be used to control the frequency of radio waves from an electronic oscillator. In 1958 a clock, based on a beam of caesium atoms, was successfully constructed on this principle. The electronic oscillator is controlled by a quartz crystal whose vibrations are in turn controlled by the effect on the beam of caesium atoms of radio waves produced by the oscillator.

As in the case of the quartz clock, it is these accurately maintained electrical oscillations which ultimately drive the clock. Comparison of the timekeeping of two of these clocks showed that atomic clocks could be relied upon to an accuracy of 1 part in 1011 over an apparently indefinite period of time. To put this in a slightly different way, this meant that they could be relied upon to within 1 second in 3 000 years!

In 1964 the international standard second became based on the atomic clock. One second was defined as 9,192, 631,770 cycles of the standard caesium-133 transition.

Global positioning

Today we take for granted that a smartphone can be located to within less than 10 metres, using time signals from a global network of artificial satellites which carry synchronised atomic clocks. GPS satellites continuously transmit their position and current time (accurate to about 14 nanoseconds).

About time

Particle physicists study fundamental particles in the Universe. Influenced by both Newton and Einstein, they are concerned not only with measuring time accurately but also with fundamental questions, such as these: ‘What is time?’, ‘Does time run steadily?’, ‘Could time run backwards?’ and ‘Would we know if it did?’

appears in the relation T^2 ∝ a^3 f=1/T
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