Physics

Physics

Problem

A 1.2 m1.2\,\text{m} long string fixed at both ends forms a standing wave pattern with exactly five nodes along its length (including the ends). Find the wavelength of the waves on the string. a) 0.30 m0.30\,\text{m} b) 2.40 m2.40\,\text{m} c) 0.60 m0.60\,\text{m} d) 0.48 m0.48\,\text{m}
Intuitive explanation

Standing waves on a fixed string only "fit" when an integer number of half-wavelengths spans the length—that's the key constraint. Since nodes mark the points where the wave is always zero, counting nodes tells you directly how many half-wavelengths you have: five nodes means four segments between them, each one half a wavelength. Use this relationship to solve for λ\lambda.

Intuitive explanation

Standing waves on a fixed string only "fit" when an integer number of half-wavelengths spans the length—that's the key constraint. Since nodes mark the points where the wave is always zero, counting nodes tells you directly how many half-wavelengths you have: five nodes means four segments between them, each one half a wavelength. Use this relationship to solve for λ\lambda.

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