Question

At what tension, in newtons, must the D-string must be stretched in order for it to be properly tuned

Answer 1

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 19.718 Newtons

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;

$\displaystyle f_1 \cdot \lambda _1 =\mathbf{ \sqrt{\frac{T}{m/L} }}$

Therefore;

$\displaystyle T = \mathbf{\frac{f_1^2 \cdot \lambda _1^2 \cdot m }{L}}$

Which gives;

$\displaystyle T = \frac{146.8^2 \times 0.61^2 \times 1.5 \times 10^{-3} }{0.61 } \approx \mathbf{19.718}$

The tension to which the D-string must be tuned, T ≈ 19.718 Newtons

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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.