For transverse waves traveling along a string or rope, there is a nice formula for the velocity of the waves in terms of the tension and the linear mass density. The formula is v = sqrt(T/u) where T is the tension and u is the linear mass density.
In our case, the tension is T = 1200 N and the linear density can be computed by dividing the mass of the string by it's length: u = (5 g)/(150 cm) = 1/30 g/cm. We need to be careful about units here. Since 1 N = 1 kg m/s^2, it would be helpful to have the units of mass density in kg/m instead of g/cm. This is because we want to use compatible units when dividing T by u. Using dimensional analysis, we can convert u to the right units as follows: u = (1/30 g/cm)*(1 kg/1000 g)*(100 cm)/(1 m) = (1/30)*(100/1000) kg/m = 1/300 kg/m. It's nice to keep things in fractions rather than decimals until the very end of the calculation because it will be easier to do calculatons.
Using our formula for velocity, we have v = sqrt[(1200 kg m/s^2)/(1/300 kg/m)] = sqrt(360,000 m^2/s^2) = 600 m/s. So now we know the velocity of transverse waves on the string is 600 m/s.
To compute the fundamental frequency of the string, we imagine both ends of the string as fixed and think about what is the largest wavelength for a wave that could "fit" on the string. The smallest "part" of a wave that could have both ends fixed is half of wavelength so the biggest wave we can "fit" on the string with both ends fixed is a wave whose half wavelength is the entire length of the string. So (1/2) L = 150 cm or the wavelength L = 300 cm = 3 m.
The fundamental frequency is the frequency of a wave which has this wavelength. Wavelength and frequency are related by the formula v = f L where v is the wave velocity, f is the frequency, and L is the wavelength. In our case, v = 600 m/s and L = 3 m. Therefore, the fundamental frequency is f = (600 m/s)/(3 m) = 200 1/s or 200 Hz.
