Frequency Physics Example 4

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Example 4

medium

A guitar string vibrates at a fundamental frequency of

330 \text{ Hz}

. What are the frequencies of the second and third harmonics? If the string length is

0.65 \text{ m}

, what is the wavelength of the fundamental?

Solution

1
Harmonics are integer multiples of the fundamental: 2nd harmonic = $2 \times 330 = 660 \text{ Hz}$ . 3rd harmonic = $3 \times 330 = 990 \text{ Hz}$ .
2
For a string fixed at both ends, the fundamental wavelength is twice the string length: $\lambda_1 = 2L = 2 \times 0.65 = 1.30 \text{ m}$ .

Answer

f_2 = 660 \text{ Hz}, \; f_3 = 990 \text{ Hz}, \; \lambda_1 = 1.30 \text{ m}

A vibrating string produces a fundamental and harmonics (overtones). The fundamental has one antinode; each higher harmonic adds another antinode, shortening the wavelength and increasing the frequency by integer multiples.

About Frequency

The number of complete wave cycles passing a fixed point per second, measured in hertz (Hz).

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More Frequency Examples

Example 1 easy

A pendulum completes [formula] swings in [formula]. What is its frequency and period?

Example 2 medium

A radio station broadcasts at [formula]. What is the wavelength of the radio wave? Use [formula].

Example 3 easy

A wave has a period of [formula]. What is its frequency?

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