On a violin, a correctly tuned A string has a frequency of 420 Hz. If an A string produces sound at 490 Hz und

Question

On a violin, a correctly tuned A string has a frequency of 420 Hz. If an A string produces sound at 490 Hz under a tension of 490 N, what should the tension be to produce the correct frequency?

N

Answer 1

Most orchestras tune to A440, not 420, and some go even higher than that. ("Concert" pitch.)

Answer 2

The speed of a transverse wave in a stretched string is

v = sqrt(F/dens)

where F is the tension

'dens' is the mass density of the string -- constant in this case

Since the length of vibrating part of the string is constant, the wavelength is fixed and the frequency is directly proportional to the velocity.

(Remember: wavelength * frequency = velocity)

So the frequency is proportional to the square root of the tension

freq = a sqrt(F)

490 = a sqrt(490)

a = sqrt(490)

420 = sqrt(490) sqrt(F)

F = 420^2 /490 = 360 N