The fundamental frequency, wavelength of the wave, and mass per unit
length of the string, determines the tension in the string.
- The tension to which the D-string must be tuned is approximately <u>19.718 Newtons</u>
Reasons:
From a similar question, we have;
Fundamental frequency, f₁ = 146.8 Hz
Oscillating length on the D-string, λ₁ = 0.61 m
Mass of the string = 1.5 × 10⁻³ kg.
We have;
![\displaystyle f_1 \cdot \lambda _1 =\mathbf{ \sqrt{\frac{T}{m/L} }}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_1%20%5Ccdot%20%5Clambda%20_1%20%3D%5Cmathbf%7B%20%5Csqrt%7B%5Cfrac%7BT%7D%7Bm%2FL%7D%20%7D%7D)
Therefore;
![\displaystyle T = \mathbf{\frac{f_1^2 \cdot \lambda _1^2 \cdot m }{L}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20T%20%3D%20%20%5Cmathbf%7B%5Cfrac%7Bf_1%5E2%20%5Ccdot%20%5Clambda%20_1%5E2%20%5Ccdot%20m%20%7D%7BL%7D%7D)
Which gives;
![\displaystyle T = \frac{146.8^2 \times 0.61^2 \times 1.5 \times 10^{-3} }{0.61 } \approx \mathbf{19.718}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20T%20%3D%20%20%5Cfrac%7B146.8%5E2%20%5Ctimes%200.61%5E2%20%5Ctimes%201.5%20%5Ctimes%2010%5E%7B-3%7D%20%7D%7B0.61%20%7D%20%5Capprox%20%20%5Cmathbf%7B19.718%7D)
The tension to which the D-string must be tuned, T ≈ <u>19.718 Newtons</u>
Learn more here:
brainly.com/question/15589287
The parameters given in a similar question obtained online are;
The fundamental frequency of the tone, f₁ = 146.8 Hz
The oscillating length on the D-string, λ₁ = 0.61 m
The mass of the string = 1.5 × 10⁻³ kg.