envelope curve

简明释义

包络线

英英释义

例句

1.Musicians often use the envelope curve to shape the dynamics of their performances.

音乐家常常使用包络曲线来塑造他们表演的动态。

2.The envelope curve in this graph illustrates the maximum and minimum values of the data set.

此图中的包络曲线展示了数据集的最大值和最小值。

3.In signal processing, analyzing the envelope curve can help identify key features of the signal.

在信号处理中，分析包络曲线可以帮助识别信号的关键特征。

4.The envelope curve of a stock price can show the overall trend and volatility in the market.

股票价格的包络曲线可以显示市场的整体趋势和波动性。

5.The envelope curve of the sound wave indicates its maximum amplitude over time.

声音波的包络曲线表示其最大振幅随时间的变化。

作文

In mathematics and physics, the concept of an envelope curve is quite fascinating. It refers to a curve that is tangent to a family of curves at each point. This means that the envelope curve effectively 'envelopes' or surrounds a set of curves, touching them at specific points without crossing them. Understanding this concept can be crucial in various fields, such as engineering, optics, and even economics. For instance, in engineering, the envelope curve can help in determining the limits of performance for different systems. By analyzing the envelope curve, engineers can identify the maximum and minimum values that certain parameters can take, ensuring optimal design and functionality.In the realm of optics, the envelope curve plays a vital role in the study of waveforms. When dealing with light waves or sound waves, the envelope curve represents the modulation of the amplitude over time. This is particularly important in telecommunications, where understanding the envelope curve can lead to better signal processing techniques. By examining the envelope curve, engineers can improve the clarity and quality of transmitted signals, ensuring that information is conveyed accurately.Economics also benefits from the application of the envelope curve. In this field, it can be used to analyze supply and demand curves, helping economists understand consumer behavior and market dynamics. The envelope curve can illustrate the maximum potential output of a market under certain conditions, providing insights into how resources are allocated efficiently.To visualize the envelope curve, consider a simple example involving a series of parabolas. Imagine multiple parabolas opening upwards, each with a different vertex. The envelope curve would be the line that just touches the highest points of each parabola, indicating the upper limit of the combined curves. This visualization helps reinforce the idea that the envelope curve serves as a boundary that encapsulates the behavior of the set of curves it surrounds.Moreover, the mathematical formulation of the envelope curve can be derived using calculus. By taking derivatives of the functions that define the family of curves, one can find points of tangency and thus construct the envelope curve. This process not only enhances our understanding of the curves involved but also deepens our appreciation for the interconnectedness of mathematical concepts.In conclusion, the envelope curve is more than just a mathematical abstraction; it has practical applications across various disciplines. Whether in engineering, optics, or economics, the envelope curve provides valuable insights that can lead to advancements and improvements in technology and understanding. Embracing the concept of the envelope curve allows us to appreciate the beauty of mathematics and its relevance to the real world, reinforcing the idea that mathematics is not merely theoretical but deeply intertwined with the fabric of our daily lives.

在数学和物理学中，包络曲线的概念相当迷人。它指的是在每一点上与一系列曲线相切的曲线。这意味着包络曲线有效地“包围”或环绕一组曲线，在特定点触摸它们而不交叉。理解这一概念在工程、光学甚至经济学等各个领域都至关重要。例如，在工程中，包络曲线可以帮助确定不同系统的性能极限。通过分析包络曲线，工程师可以识别某些参数可以取的最大值和最小值，从而确保最佳设计和功能。在光学领域，包络曲线在波形研究中发挥着重要作用。当处理光波或声波时，包络曲线表示幅度随时间的调制。这在电信中尤为重要，因为理解包络曲线可以导致更好的信号处理技术。通过检查包络曲线，工程师可以改善传输信号的清晰度和质量，确保信息准确传递。经济学也受益于包络曲线的应用。在这一领域，它可以用来分析供需曲线，帮助经济学家理解消费者行为和市场动态。包络曲线可以说明在特定条件下市场的最大潜在产出，为资源的有效配置提供洞见。为了可视化包络曲线，考虑一个涉及一系列抛物线的简单例子。想象多条向上开口的抛物线，每条抛物线都有不同的顶点。包络曲线将是刚好触碰每条抛物线最高点的线，表示组合曲线的上限。这种可视化有助于加强这样的观点：包络曲线作为一个边界，封装了它所包围的一组曲线的行为。此外，包络曲线的数学公式可以通过微积分推导出来。通过对定义曲线族的函数进行求导，可以找到切点，从而构建包络曲线。这个过程不仅增强了我们对涉及的曲线的理解，也加深了我们对数学概念相互关联性的欣赏。总之，包络曲线不仅仅是一个数学抽象；它在各个学科中具有实际应用。无论是在工程、光学还是经济学中，包络曲线提供了有价值的洞见，能够推动技术和理解的进步。接受包络曲线的概念使我们能够欣赏数学之美及其与现实世界的相关性，强化了数学不仅仅是理论，而是与我们日常生活的结构紧密相连的观点。