Problem 15.62 A vertical, 1.23-m length of 18-gauge (diameter of 1.024 mm) coppe
ID: 1497525 • Letter: P
Question
Problem 15.62 A vertical, 1.23-m length of 18-gauge (diameter of 1.024 mm) copper wire has a 150.0-N ball hanging from it.
Part A
What is the wavelength of the third harmonic for this wire?
m
Part B
A 750.0-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? (Hint: See Table 11.1 in the textbook for Young's modulus.)
Express your answer using two significant figures.
=m
Part B
A 750.0-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? (Hint: See Table 11.1 in the textbook for Young's modulus.)
Express your answer using two significant figures.
= mmExplanation / Answer
a)
The 3rd harmonic occurs when n(/2) = L (wire length).
= 2L/3 = 1.5*1.23 = 0.82 m
b)
Delta wavelength = Delta Force / ( Cross sectional Area A * Youngs modulus of copper)
= (750-150)/pi*(1.024*10^-3)^2 *1.2*10^11)/4 = 5.5 mm