Question

The D-string on a properly tuned guitar produces a tone with a fundamental frequency of 146.8 Hz. The oscillating length of a D-string on a certain guitar is 0.65 m. This same length of string is weighed and found have a mass of 1.4×10-3 kg.

25% Part (a) At what tension, in newtons, must the D-string must be stretched in order for it to be properly tuned? T = 78.443 T = 78.44     ✔ Correct!   25% Part (b) What is the wavelength, in meters, of the standing wave in the D-string when it is oscillating at its third harmonic (also called its second overtone)? λ3 = 0.43     ✔ Correct!
25% Part (c) Determine the frequency, in hertz, of the third harmonic of the tone produced by the properly tuned D-string.
f3 = 146.7973| sin() cos() tan() cotan() asin() acos() atan() acotan() sinh() cosh() tanh() cotanh() Degrees  Radians π ( ) 7 8 9 HOME E ↑^ ^↓ 4 5 6 ← / * 1 2 3 → + - 0 . END √() BACKSPACE DEL CLEAR		Grade Summary Deductions 6% Potential 94% Submissions Attempts remaining: 3 (3% per attempt) detailed view 1 3% 2 3%
Hints:  1  for a  0%  deduction. Hints remaining:  0 -Use the formula for a harmonic of a stretched string in terms of the fundamental frequency and the harmonic number.	Feedback:  0%  deduction per feedback.
25% Part (d) The guitarist shortens the oscillating length of the properly tuned D-string by 0.15 m by pressing on the string with a finger. What is the fundamental frequency, in hertz, of the new tone that is produced when the string is plucked?