If you increase tension while holding length and mass constant, what happens to the frequency?

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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

If you increase tension while holding length and mass constant, what happens to the frequency?

Explanation:
The key idea is that the pitch of a vibrating string depends on how fast waves travel along it. The wave speed on a string is v = sqrt(T/μ), where T is tension and μ is mass per unit length. If length and mass are fixed, μ stays the same, so increasing tension makes the wave speed increase as the square root of T. The fundamental frequency for a string fixed at both ends is f1 = v/(2L). Since v increases with tension, f1 also increases (by the square root of T). All higher harmonics scale the same way, so they shift to higher frequencies rather than disappearing. So increasing tension causes the frequency to increase.

The key idea is that the pitch of a vibrating string depends on how fast waves travel along it. The wave speed on a string is v = sqrt(T/μ), where T is tension and μ is mass per unit length. If length and mass are fixed, μ stays the same, so increasing tension makes the wave speed increase as the square root of T. The fundamental frequency for a string fixed at both ends is f1 = v/(2L). Since v increases with tension, f1 also increases (by the square root of T). All higher harmonics scale the same way, so they shift to higher frequencies rather than disappearing. So increasing tension causes the frequency to increase.

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