Question

Question #d5420

Answer 1

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"`.