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Two carpenters are hammering at the same time, each at a different hammering frequency. The hammering frequency is the number of hammer blows per second. Every 4.6 s, both carpenters strike at the same instant, producing an effect very similar to a beat frequency. The first carpenter strikes a blow every 0.75 s. How many seconds elapse between the second carpenter's blows if the second carpenter hammers (a) more rapidly than the first carpenter, and (b) less rapidly than the first carpenter?

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