Question

A vertical, 1.14-m length of 18-gauge (diameter of 1.024 mm) copper wire has a 140.0-N ball hanging from it. A 700.0-N ball now replaces the original ball. What is the change in the wavelength of the third harmonic caused by replacing the light ball with the heavy one?

Answer 1

Wavelength of standing wave is given by:

lambda = 2*L/n

when the wavelength changes the change in length is given by:

dL = F*L/(A*Y)

for the third harmonic n = 3

Y = young's modulus for copper = 11*10^10 Pa

A = pi*r^2 = pi*(1.024*10^-3)^2/4

Now change in length when 140 N is replaced by 700 N will be

dL = dF*L/A*Y

dL = (700 - 140)*1.14/[(pi*(1.024*10^-3)^2/4)*11*10^10]

dL = 7.047*10^-3 m

So,

Change in wavelength will be

d(lambda) = 2*dL/3

= 2*7.047*10^-3/3 = 4.69*10^-3 m

change in wavelengh = 4.69 mm