91Ó°ÊÓ

Frequency is a fundamental concept when it comes to understanding how sound waves operate. It tells us how often the peaks of the wave pass a certain point per second. For the quartz oscillator in our exercise, we are interested in calculating how many times it vibrates per second. This value is known as the frequency and is measured in Hertz (Hz).
To find the frequency, we use the formula that links speed of sound, wavelength, and frequency:

• Speed of sound (\(v\)) = Frequency (\(f\)) × Wavelength (\(\lambda\))

By rearranging this formula, we find the frequency with:

• Frequency, \(f = \frac{v}{\lambda}\)

In our exercise, the speed of sound in quartz is given as 3700 m/s. By calculating the wavelength correctly, which is 0.0141 m, we divide speed by wavelength using the formula to get the frequency:\[ f = \frac{3700}{0.0141} \approx 262411.35\text{ Hz}\]This tells us the quartz crystal oscillates about 262,411 times per second!

Wavelength is the distance between two consecutive similar points of a wave, like peak to peak or trough to trough. In the context of our quartz oscillator, the wavelength corresponds to the length between two consecutive antinodes. However, the given distance between the antinodes in the exercise is only half of the full wavelength because the wave is also passing through a node in between.
For the quartz oscillator example, the provided distance is 7.05 mm, but because this measures only from antinode to antinode, it represents half of the wave. This midpoint, known as a node, divides the wave into two equal halves. Therefore, to get the full wavelength, we double that distance.

• Half wavelength (\(\lambda/2\)) = 0.00705 m
• Full wavelength (\(\lambda\)) = 2 × 0.00705 m = 0.0141 m

Having determined the correct full wavelength, it becomes simple to further calculate the frequency of vibration or to understand other wave properties.

A quartz oscillator is a fascinating device, integral to how many electronic clocks and watches keep time. Quartz crystals have this unique ability to oscillate or vibrate at a constant frequency when subjected to mechanical stress – a property known as piezoelectricity.
In the exercise, we use a quartz block oscillator oscillating by contraction and expansion. The specific conditions caused by sound waves within the quartz help this oscillation maintain accuracy and consistency. The crystal features two crucial areas known as antinodes, where the displacement of air particles is maximum, and nodes where there is minimal to no movement. By ensuring these vibrations remain steady, quartz watches can keep incredibly accurate time, significantly better than older mechanical watch technologies.

Vibrations are a key aspect of wave behavior, especially when discussing how quartz oscillators work. When you hear sound, you've experienced vibrations traveling through a medium (like quartz or air). In our quartz block, vibrations imply a back-and-forth movement of the block particles between the antinodes. This movement might be too brief and rapid for human perception.
Quartz's ability to vibrate comes from its piezoelectric properties. When mechanical stress such as pressure is applied to quartz, its internal electrical charges deform and generate an electric field. This field can lead to mechanical wave vibrations within the crystal.

• At antinodes, particles of quartz oscillate with maximum amplitude.
• At the node, there is minimal movement.

These characteristics allow the useful conversion of mechanical energy into electrical energy and vice versa, enabling modern watches to keep time and electronic circuits to function properly.