fundamental mode

简明释义

主振动形式

英英释义

例句

1.The fundamental mode 基模 of a laser determines its coherence and beam quality.

激光的基模决定了其相干性和光束质量。

2.In a vibrating string, the fundamental mode 基模 is the simplest form of vibration.

在一个振动的弦中，基模是最简单的振动形式。

3.In optics, the fundamental mode 基模 refers to the lowest order mode of light propagation in a fiber.

在光学中，基模指的是光在光纤中传播的最低阶模态。

4.The fundamental mode 基模 of a drum produces the lowest pitch sound.

鼓的基模产生最低音调的声音。

5.When analyzing the vibrations of a beam, engineers often focus on the fundamental mode 基模 first.

在分析梁的振动时，工程师通常首先关注基模。

作文

In the study of physics and engineering, the term fundamental mode refers to the simplest and most basic form of vibration or oscillation that a system can exhibit. It is the lowest frequency at which a system naturally resonates. Understanding the fundamental mode is crucial for various applications, including structural engineering, acoustics, and even quantum mechanics. For instance, when analyzing the vibrations of a guitar string, the fundamental mode corresponds to the lowest pitch produced when the string vibrates freely without any nodes other than at its endpoints.The significance of the fundamental mode extends beyond mere theoretical interest; it has practical implications in designing buildings and bridges to withstand seismic activity. Engineers must consider how structures will respond to vibrations caused by earthquakes, and identifying the fundamental mode helps them predict and mitigate potential damage. By ensuring that the natural frequency of a building does not coincide with the frequencies of expected ground motion, engineers can enhance the safety and durability of their designs.Moreover, the concept of the fundamental mode is not limited to physical structures. In acoustics, musical instruments produce a range of frequencies, but the fundamental mode determines the instrument's primary tone. For example, in wind instruments, the length and shape of the air column influence the fundamental mode, ultimately affecting the sound produced. Musicians often manipulate their instruments to emphasize different harmonics, but the fundamental mode remains the foundation upon which all other tones are built.In the realm of quantum mechanics, the fundamental mode also plays a pivotal role. Particles such as electrons exhibit wave-like behavior, and their fundamental mode corresponds to the lowest energy state they can occupy. This concept is essential for understanding phenomena such as superconductivity and quantum entanglement. Researchers explore how particles transition between different modes, revealing insights into the fundamental nature of matter and energy.The mathematical representation of the fundamental mode often involves differential equations and eigenvalue problems. For example, in a vibrating string, the fundamental mode can be described using a sine function, where the wave's wavelength is twice the length of the string. This elegant relationship highlights the interconnectedness of mathematics and physical phenomena, showcasing how abstract concepts can provide tangible insights into the world around us.In conclusion, the fundamental mode is a foundational concept across multiple disciplines, from engineering to music and quantum physics. Its influence permeates various fields, guiding practitioners in understanding and manipulating systems to achieve desired outcomes. Recognizing the importance of the fundamental mode allows us to appreciate the intricate relationships between natural phenomena and human-made structures, ultimately leading to safer buildings, better musical performances, and deeper insights into the universe. As we continue to explore the complexities of our world, the fundamental mode will undoubtedly remain a key concept in our journey of discovery.

在物理和工程学的研究中，术语fundamental mode指的是一个系统可以表现出的最简单和最基本的振动或振荡形式。它是系统自然共振的最低频率。理解fundamental mode对于各种应用至关重要，包括结构工程、声学，甚至量子力学。例如，在分析吉他弦的振动时，fundamental mode对应于当弦自由振动而没有其他节点（除了端点）时产生的最低音调。fundamental mode的重要性不仅限于理论兴趣；它在设计建筑和桥梁以抵御地震活动方面具有实际意义。工程师必须考虑结构如何响应由地震引起的振动，而识别fundamental mode有助于他们预测和减轻潜在的损害。通过确保建筑的自然频率与预期地面运动的频率不重合，工程师可以增强其设计的安全性和耐久性。此外，fundamental mode的概念并不限于物理结构。在声学中，乐器产生一系列频率，但fundamental mode决定了乐器的主要音调。例如，在管乐器中，空气柱的长度和形状影响fundamental mode，最终影响所产生的声音。音乐家通常操控他们的乐器以强调不同的谐波，但fundamental mode仍然是所有其他音调构建的基础。在量子力学领域，fundamental mode也发挥着关键作用。电子等粒子表现出波动行为，它们的fundamental mode对应于它们可以占据的最低能量状态。这个概念对于理解超导现象和量子纠缠至关重要。研究人员探索粒子如何在不同模式之间过渡，从而揭示物质和能量的基本性质。fundamental mode的数学表示通常涉及微分方程和特征值问题。例如，在振动弦中，fundamental mode可以用正弦函数描述，其中波长是弦长度的两倍。这种优雅的关系突显了数学和物理现象之间的相互联系，展示了抽象概念如何提供对我们周围世界的具体见解。总之，fundamental mode是多个学科中的基础概念，从工程到音乐再到量子物理。它的影响渗透到各个领域，指导从业者理解和操纵系统以达到期望的结果。认识到fundamental mode的重要性使我们能够欣赏自然现象与人造结构之间复杂的关系，最终导致更安全的建筑、更好的音乐表演以及对宇宙更深刻的洞察。随着我们继续探索我们世界的复杂性，fundamental mode无疑将继续成为我们发现之旅中的关键概念。