In a simple vibrating string, what happens to the frequency as string length increases?

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Explore the Psychology of Music Test. Prepare with interactive quizzes. Use multiple-choice questions and explanations to enhance your understanding and get ready for your test.

Multiple Choice

In a simple vibrating string, what happens to the frequency as string length increases?

Explanation:
In a simple string fixed at both ends, the fundamental mode has a wavelength that is twice the length of the string, so λ = 2L. The wave speed v is determined by the tension and the string’s linear density (v = √(T/μ)). Frequency is the speed divided by wavelength, f = v/λ, which for the fundamental becomes f = v/(2L). Therefore, as the length L increases while tension and density stay the same, the frequency decreases. This matches the intuition that a longer string vibrates more slowly, producing a lower pitch.

In a simple string fixed at both ends, the fundamental mode has a wavelength that is twice the length of the string, so λ = 2L. The wave speed v is determined by the tension and the string’s linear density (v = √(T/μ)). Frequency is the speed divided by wavelength, f = v/λ, which for the fundamental becomes f = v/(2L). Therefore, as the length L increases while tension and density stay the same, the frequency decreases. This matches the intuition that a longer string vibrates more slowly, producing a lower pitch.

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