Physics Question & Answer Key

Question:

A vibrating string on a violin is 330 mm long and has a fundamental frequency of 659 Hz. Tge string is then pressed on against the fingerboard at a point of 60 mm from its end.
a) Calculate the fundamental frequency when the string is pressed against the fingerboard. 
b) Calculate the wavelength of the sound wave produced. 
c) Calculate the frequency of the next two harmonics. 


Answer:

f = 659 Hz
L = 0.33 m
L_{1 = 0.33 - 0.06 = 0.27 m}

a) 

v = λf
   = (659)(2)(0.33)
   = 434.94 m/s

f_{1= (434.94) / (2)(0.27)}

   _{= 805 Hz}

_b) 

λ = v / f
   = (343) / (805)
   = 0.43 m

c)

f_{2 = (2)(434.94) / (2)(0.27)}

    _{= 1611 Hz}

f_{3 = (3)(434.94) / (2)(0.27)}

    _{= 2416 Hz}