Question Details Two carpenters are hammering at the same time, each at a differ

Question

Question Details
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 3.72 s, both carpenters strike at the same instant, producing an effect very similar to a beat frequency. The first carpenter strikes a blow every 0.62 s.
(a) How many seconds elapse between the second carpenter's blows if the second carpenter hammers more rapidly than the first carpenter?
s

(b) How many seconds elapse between the second carpenter's blows if the second carpenter hammers less rapidly than the first carpenter?
s

Please provide explanation and answer, thanks.

Explanation / Answer

(a)    Here , we have a 2 values

    If second carpenter more rapid than first carpenter

change of Thier frequencies = n_B difference n_A =   1/4.25 = 0.235   Hz

frequency of first carpenters = n_A = 1/0.85 = 1.176 Hz

Thus, frequency of second carpeners = n_B = 1.176 + 0.235 = 1.411 Hz

       Time = 1/ 1.411   = 0.708 sec

0.708 seconds elapse between the second carpenter's blows If second carpenter more rapid than first carpenter

(b)

If second carpenter less rapid than first carpenter

change of Thier frequencies = n_A difference n_B =   1/4.25 = 0.235   Hz

frequency of first carpenters = n_A = 1/0.85 = 1.176 Hz

Thus, frequency of second carpeners = n_B = 1.176 - 0.235 = 0.941 Hz

       Time = 1/ 0.941 = 1.062 sec

1.062    seconds elapse between the second carpenter's blows If second carpenter less rapid than first carpenter

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