The frequency of a tuning fork can be found by the method...

The frequency of a tuning fork can be found by the method shown in Figure 13-24. A long tube open at both ends is submerged in a beaker of water, and the vibrating tuning fork is placed near the top of the tube. The length of the air column, $L,$ is adjusted by moving the tube vertically. The sound waves generated by the fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube. The largest value for $L$ for which a peak occurs in sound intensity is $9.00 \mathrm{cm} .$ (Use $345 \mathrm{m} / \mathrm{s}$ as the speed of sound in air.) a. What is the frequency of the tuning fork? b. What is the value of $L$ for the next two harmonics?

The frequency of a tuning fork can be found by the method shown in Figure 13-24. A long tube open at both ends is submerged in a beaker of water, and the vibrating tuning fork is placed near the top of the tube. The length of the air column, $L,$ is adjusted by moving the tube vertically. The sound waves generated by the fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube. The largest value for $L$ for which a peak occurs in sound intensity is $9.00 \mathrm{cm} .$ (Use $345 \mathrm{m} / \mathrm{s}$ as the speed of sound in air.) a. What is the frequency of the tuning fork?
b. What is the value of $L$ for the next two harmonics?

Key Concepts

Standing Waves

Standing waves are patterns that form when two waves of the same frequency and amplitude travel in opposite directions and interfere, resulting in nodes (points of zero amplitude) and antinodes (points of maximum amplitude). In the context of air columns, standing waves are established when the dimensions of the column allow the sound waves to reinforce themselves through constructive interference, which is fundamental to understanding resonance.

Resonance in Air Columns

Resonance in air columns occurs when the length of the column supports a standing wave pattern that matches a natural frequency of the system. When the frequency of the sound source, such as a tuning fork, coincides with one of the resonant frequencies of the air column, the resulting wave is amplified. This phenomenon is exploited to determine properties like the wavelength, and hence the frequency, of the sound source.

Harmonics

Harmonics refer to the discrete frequencies at which resonance occurs in a system, corresponding to different standing wave patterns. In air columns, the harmonic sequence depends on the boundary conditions—whether the tube is closed at one end or open at both ends. Each harmonic represents a mode of vibration with a specific relationship between the wavelength and the length of the air column.

Relationship between Frequency, Wavelength, and Speed of Sound

The fundamental relationship between frequency (f), wavelength (?), and the speed of sound (v) is expressed by the equation f = v/?. This relationship is crucial in experiments using resonance, as measuring the resonant length of an air column allows one to determine the wavelength, and, with the known speed of sound, to calculate the frequency of the sound source.

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