Question

A violin string of length 43 cm and mass 1.1 g has a frequency of 495 Hz when it is vibrating in its fundamental mode.

(a) What is the wavelength of the standing wave on the string?
  cm

(b) What is the tension in the string?
  N

(c) Where should you place your finger to increase the frequency to 645 Hz?
  cm from the fixed end of the string (from the peg of the violin)

Answer 1

A)

Linear mass density, u = m/L

u = 0.0011/0.43 = 0.00256 kg/m

Velocity, v = 2 x 0.43 x 495 = 425.7 m/s

Wavelength, lambda = v/f = 425.7/495 = 0.86 m

B)

Tension, T = v^2 u

T = 425.7^2 x 0.00256 = 463.92 N

C)

Wavelength, lambda = 425.7/645 = 0.66 m

Length, L = (0.86 - 0.66)/2 = 0.1 m = 10 cm

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