Question #d5420

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Answer 1 · 2017-05-02T08:23:21

Because the ends are fixed, standing waves can be made with any integer number of half wavelengths, ie for rope length #L#:

#L = n lambda_n /2, n in ZZ^+ implies lambda_n = (2L)/n#.

Comparing the 5m and 4m wavelengths, which we are told are consecutive harmonics, ie they are #lambda_n# and #lambda_(n+1)#:

#5/4 = ((2L)/n)/((2L)/(n+1)) implies n = 4#

#implies lambda_4 = 5 = (2L)/4 implies L = 10" m"#

And to check:

#implies lambda_5 = 4 = (2L)/(4+1) implies L = 10" m"#

For (ii), #M = rho L = 6" kg"#.

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