envolope curve

简明释义

包络线

英英释义

例句

1.In audio engineering, understanding the envelope curve is crucial for shaping the sound's attack and decay.

在音频工程中，理解包络曲线对于塑造声音的起音和衰减至关重要。

2.When designing synthesizers, engineers often manipulate the envelope curve to achieve desired sound effects.

在设计合成器时，工程师通常会调整包络曲线以实现所需的音效。

3.The envelope curve of the signal shows how the amplitude changes over time.

信号的包络曲线显示了幅度随时间变化的情况。

4.The artist used the envelope curve to define the dynamics of the sound in her composition.

这位艺术家使用了包络曲线来定义她作品中声音的动态。

5.The envelope curve is a critical aspect of sound synthesis that affects how we perceive sounds.

包络曲线是声音合成的一个关键方面，影响我们对声音的感知。

作文

In the field of mathematics and engineering, the concept of an envelope curve plays a critical role in understanding the behavior of various functions and systems. An envelope curve can be defined as a curve that is tangent to a family of curves at each point, essentially outlining the limits of those curves. This concept is not only theoretical but also has practical applications in physics, economics, and even art. For instance, in physics, the envelope curve can illustrate the maximum displacement of a wave or signal over time, providing insights into its amplitude and frequency characteristics.One of the most common examples of an envelope curve can be found in the study of oscillatory motion. When we analyze the motion of a pendulum or a mass on a spring, we observe that the position of the object varies over time, creating a sinusoidal wave pattern. The envelope curve in this case would represent the maximum height reached by the pendulum or the maximum stretch of the spring. By studying this envelope curve, engineers can design systems that operate within safe limits, ensuring that they do not exceed the maximum allowable displacement.In economics, the envelope curve can be used to represent the production possibilities frontier (PPF). The PPF illustrates the maximum output combinations of two goods that can be produced with available resources. The envelope curve in this context helps economists understand the trade-offs between different goods and services, guiding decision-making processes regarding resource allocation. By analyzing shifts in the envelope curve, economists can infer changes in technology, resource availability, or consumer preferences.Moreover, the envelope curve is also significant in the realm of art and design. Artists often utilize the concept of an envelope curve to create visually appealing compositions. By understanding how different elements interact within a space, artists can establish a sense of balance and harmony. The envelope curve can guide the viewer's eye through the artwork, leading them to focus on key areas while maintaining an overall coherence in the piece.To fully grasp the implications of an envelope curve, one must consider its mathematical foundations. The construction of an envelope curve often involves calculus, particularly the use of derivatives to find points of tangency between curves. By solving equations that represent the family of curves, mathematicians can derive the envelope curve and analyze its properties. This analytical approach allows for a deeper understanding of the relationships between different functions and their behaviors.In conclusion, the concept of an envelope curve is a powerful tool across various disciplines, including mathematics, physics, economics, and art. Its ability to outline the boundaries of a set of curves provides valuable insights that can lead to better designs, more informed economic policies, and aesthetically pleasing artworks. As we continue to explore the applications of the envelope curve, it becomes increasingly clear that this mathematical concept is integral to our understanding of the world around us.

在数学和工程领域，包络曲线的概念在理解各种函数和系统的行为中发挥着关键作用。包络曲线可以定义为与一组曲线在每个点上相切的曲线，基本上勾勒出这些曲线的极限。这个概念不仅是理论上的，而且在物理、经济甚至艺术中有实际应用。例如，在物理学中，包络曲线可以说明波或信号随时间变化的最大位移，为其振幅和频率特性提供见解。包络曲线的一个常见例子可以在振动运动的研究中找到。当我们分析摆动或弹簧上的质量的运动时，我们观察到物体的位置随时间变化，产生正弦波模式。在这种情况下，包络曲线将代表摆锤达到的最大高度或弹簧的最大伸展。通过研究这个包络曲线，工程师可以设计在安全范围内运行的系统，确保它们不会超过允许的最大位移。在经济学中，包络曲线可以用来表示生产可能性边界（PPF）。PPF描绘了在可用资源下可以生产的两种商品的最大产出组合。在这种情况下，包络曲线帮助经济学家理解不同商品和服务之间的权衡，指导资源分配的决策过程。通过分析包络曲线的变化，经济学家可以推测技术、资源可用性或消费者偏好的变化。此外，包络曲线在艺术和设计领域也具有重要意义。艺术家通常利用包络曲线的概念来创造视觉上吸引人的作品。通过理解不同元素在空间中的互动，艺术家可以建立一种平衡和和谐感。包络曲线可以引导观众的视线穿过艺术作品，让他们关注关键区域，同时保持整体的一致性。要充分理解包络曲线的含义，必须考虑其数学基础。包络曲线的构造通常涉及微积分，特别是使用导数来寻找曲线之间的切点。通过求解代表曲线族的方程，数学家可以推导出包络曲线并分析其属性。这种分析方法使我们能够更深入地理解不同函数及其行为之间的关系。总之，包络曲线的概念在数学、物理、经济和艺术等多个学科中都是一种强大的工具。它能够勾勒出一组曲线的边界，提供有价值的见解，从而导致更好的设计、更明智的经济政策和美观的艺术作品。随着我们继续探索包络曲线的应用，越来越明显的是，这一数学概念对于我们理解周围世界至关重要。