The force will remain same if the mass of each sphere is doubled and the distance between them is doubled as well.
The force of gravitation between two spheres is given by

m1= mass of first object
m2= mass of second object
r= distance between the masses
Now if each mass is doubled and the distance r is doubled as well


F'=
so F'= F
so the force remains same and is equal to 1000 N.
here since string is attached with a mass of 2 kg
so here tension force in the rope is given as

here we will have

now we will have speed of wave given as

here we will have


now we know that frequency is given as
F = 100 Hz
now wavelength is given as


so wavelength will be 0.16 m