A violin string is .32m and has a mass of .0005kg. The freqency of the note played is 440Hz. What is the speed of the wave in the string?
.5*wavelenght = L
wavelength= 2*.32m
=.64m
v=f(wavelength)
=440hz*.64m
=281.6m/s
b) where must one put one's finger to play a note with a freqency of 494Hz?
v=f*wavelenght
281.6m/s=494Hz * wavelength
wavelength= .57m
Are these correct?
Yes, your calculations are correct.
For part a), to find the speed of the wave in the string, you used the formula v = f * λ (where v is the speed, f is the frequency, and λ is the wavelength). You correctly calculated the wavelength to be 0.64m (by multiplying the string length by 2), and then multiplied it by the frequency of 440Hz to obtain a speed of 281.6m/s.
For part b), you used the same formula to calculate the wavelength needed to produce a frequency of 494Hz. You divided the speed (281.6m/s) by the desired frequency (494Hz) to find that the wavelength should be approximately 0.57m.
So overall, your calculations are correct according to the given information. Well done!