A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.003 kg/m. The wavelength of the mode of vibration with the lowest frequency is
Question
A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.003 kg/m. The wavelength of the mode of vibration with the lowest frequency is
Solution
The lowest frequency of vibration for a string (also known as the fundamental frequency or the first harmonic) occurs when the length of the string is half the wavelength. This is because the string is fixed at both ends, so it must have nodes (points of no displacement) at these points.
Given that the length of the string is 30.0 cm (or 0.3 m), the wavelength of the mode of vibration with the lowest frequency is twice this length, which is 0.6 m.
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