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Astronauts visiting planet x have a 250-cm-long string whose mass is 5.00 g. they tie the string to a support, stretch it horizontally over a pulley 2.00 m away, and hang a 4.00 kg mass on the free end. then, the astronauts begin to excite standing waves on the horizontal portion of the string. their data are as follows:

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shinmin
The solution for this problem is:
v = sqrt(T/µ) where T = m*g = 4*g and µ = 0.0055/2.5 = 0.0022kg/m 
Now L = 2 m 
For a string the frequencies are n*v/2L 
so n*v/2L = 64 and (n+1)*v/2L = 80 
Now eqn 2 divided by eqn 1 yields (n + 1)/n = 80/64 = 1.25 
=> 1.25 n = n + 1 or .25n = 1 or n = 4 
now subbing back into eqn 1 we have 4*v/2L = 64 or v = 32*L = 32*1.9 = 60.8 
So 60.8= sqrt(1.1*g/0.0022) 
so 1.1*g = 60.8^2*0.0022 = > g = 60.8^2*0.0022/1.1 = 7.39 m/s^2

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