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Chapter 14: Problem 40

A string is clamped at both ends and tensioned until its fundamental frequency is \(85 \mathrm{Hz}\). If the string is then held rigidly at its midpoint, what's the lowest frequency at which it will vibrate?

Short Answer

Expert verified
The lowest frequency at which the string will vibrate when held rigidly at its midpoint is \(170 \mathrm{Hz}\).

Step by step solution

01

Identify the fundamental frequency

The fundamental frequency of the string is given as \(85 \mathrm{Hz}\). This is the lowest frequency at which the string will vibrate when it is not interfered with.
02

Calculate the frequency when the string is held rigidly at midpoint

When the string is held rigidly at its midpoint, it forms two halves that vibrate at twice the fundamental frequency. This is known as the second harmonic. Hence, to get the new frequency, we simply multiply the fundamental frequency by 2. Mathematically, it would be represented as \(2 \times 85 \mathrm{Hz} = 170 \mathrm{Hz}\).

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