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------------------------------------------------ A guitar string has a mass per unit length of 2.35 g/m. If the string is vibrating between points that are 60.0 cm apart, determine the tension [tex]F[/tex] when the string is designed to play a note of 220 Hz.

The tension force F in a guitar string designed to play a note of 220 Hz, with a mass per unit length of 2.35 g/m and vibrating between points 60.0 cm apart is approximately 73.92 N.

To find the tension, we can use the formula for the wave speed (v) in terms of frequency (f) and wavelength (λ): v = fλ. The wavelength is twice the distance between the two points of vibration, so λ = 2(60.0 cm) = 120.0 cm = 1.2 m. We know the frequency is 220 Hz.

Rearranging the wave equation, we have v = fλ, and solving for v, we get v = (f/λ). The wave speed is also related to the tension (F) and the mass per unit length (μ) of the string through the formula v = √(F/μ).

Equating these two expressions for the wave speed, we have (f/λ) = √(F/μ). Plugging in the values we know, the equation becomes (220 Hz)/(1.2 m) = √(F/2.35 g/m). Squaring both sides of the equation and rearranging, we find F = (220 Hz)^2 * 2.35 g/m * (1.2 m)^2 = 73.92 N.

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