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Chapter 4: Problem 61

A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form \(d=\sin \omega t\) for the simple harmonic motion.

Short Answer

Expert verified
The equation for the simple harmonic motion using the given data is \(d=\sin(2 \pi \times 264 \cdot t)\).

Step by step solution

01

Analyze the given data

The frequency, denoted by 'f', is given as 264 vibrations per second.
02

Calculate the Angular Frequency

Angular frequency, denoted by '\(\omega\)', can be calculated using the formula \(\omega = 2 \pi f\). Substituting the value of 'f', we get \(\omega = 2 \pi \times 264\).
03

Write the equation for simple harmonic motion

With calculated '\(\omega\)', it's possible to write the simple harmonic motion equation as \(d=\sin \omega t\).

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