Distance of sound wave propagation

Sound waves with lower frequencies tend to travel longer distances primarily because of their longer wavelengths. Here is a deeper dive into why this is the case:

1. Wavelength and diffraction:

Lower frequency sound waves have longer wavelengths. When a wave encounters obstacles such as buildings, trees, or even variations in atmospheric conditions, a longer wavelength can bend or diffract around these obstacles more easily. This means that low-frequency sounds are less likely to be blocked or scattered, allowing them to travel further without being significantly disrupted.

2. Atmospheric absorption:

The medium through which sound travels - typically air - absorbs sound energy as it propagates. This absorption tends to increase with frequency; higher frequency waves, which oscillate much more rapidly, interact more intensely with air molecules, converting more of their energy into heat. Lower frequency waves, on the other hand, experience less energy loss per cycle due to these interactions. The lower the frequency, the less the absorption, and the further the sound can propagate before it becomes too weak.

3. Scattering and energy loss

Real world examples:

    Animal communication: Elephants and whales, for instance, make extensive use of low-frequency sounds (even infrasound) to communicate over vast distances. Their calls can travel for kilometers, making them ideal for long-range communication.

    Engineering and communication: In underwater communication and certain military applications, extremely low frequencies are exploited because these waves penetrate water or obstacles better than higher frequencies.

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Relationship between plants and fungi

Over millions of years, plants and fungi have co-evolved to form interactions that both mutually beneficial and, in some cases, antagonistic. One of the most well-known examples is the formation of mycorrhizae-specialized associations where fungi colonize plant roots. In these relationships, the fungi extend their hyphal networks deep into the soil, vastly increasing the surface area for water and nutrient absorption. In return, the plant supplies the fungi with carbohydrates produced during photosynthesis. The mutual exchange not only bolsters (enhances) plant nutrition - especially the uptake of essential, but often scarce, minerals like phosphorus - but also enhances the overall resilience of the ecosystem.

While many fungi contribute positively to plant growth, not every fungal interaction is beneficial. Some fungi are pathogenic. The balance between mutualism and pathogenicity in fungal-plant interactions is complex and influenced by various factors, including environmental conditions, soil composition, and the presence of other microorganisms.

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static_cast

explicit: clear and easy to understand, so that you have no doubt what is meant

In C++, float is a data type used to store floating-point numbers, which are numbers that have a decimal point. It is a single-precision type, meaning it typically occupies 4 bytes of memory and provides about 7 decimal digits of precision.

parentheses: DJ[pəˋrenθisi:z]

In C++, an expression is a combination of variables, constants, operators, and function calls that evaluates to a single value. Expressions are fundamental to programming, as they allow computations and logical operations.

implicit: suggested without being directly expressed

In C++, int32_t is a fixed-width integer type that guarantees a size of exactly 32 bits. It is defined in the <cstdint> header and ensures portability across different platforms.

In C++, uint32_t is an unsigned 32-bit integer type that guarantees a size of exactly 32 bits. It is defined in the <cstdint> header and ensures portability across different platforms.

Unsigned: Can store only non-negative values

An IDE (Integrated Development Environment) is a software application that provides comprehensive tools for coding, debugging, and compiling programs. It streamlines development by offering features like syntax highlighting, auto-completion, and integrated debugging.

In C++, a double constant refers to a floating-point constant that is stored as a double type. By default, any floating-point literal without a suffix is treated as a double.

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牽一髮動全身

sequential: following in order of time or place

Quadrant II: not urgent but important

conscience: the part of your mind that tells you whether your actions are right or wrong

    The more proactive you are, the more effectively you can exercise personal leadership and management in your life. The more effectively you manage your life, the more Quadrant II (not urgent but important) renewing activities you can do. The more you seek first to understand, the more effectively you can do for synergetic Win/Win solutions. The more you improve in any of the habits that lead to independence, the more effective you will be in interdependent situations. And renewal is the process of renewing all the habits.

作者闡述了個人成長和持續更新的重要性，並強調各種習慣如何互相影響與促進整體效能。

首先，積極主動是基礎。當你主動掌握自己的生活時，你就能更有效地行使個人領導和管理。這種主動權能讓你更有計劃地安排時間和資源，而不是被外在情況所左右。正因為你能夠自主管理，便有餘裕去從事那些「不緊急但非常重要」的活動，它們能幫助你進行自我再增值與成長。

其次，「先求理解，再求被理解」的原則強調了良好溝通的重要性。當你學會耐心傾聽，真正理解別人的觀點時，你就更能夠找到雙贏的解決方案。這不僅促進了彼此間的協同效應，也讓合作變得更加順暢和高效。

此外，只要你不斷提升自己的獨立自主能力，在與他人互相合作時，你就能表現得更好。這意味著，個人的獨立成長是合作與共贏的基石；建立堅實的自我基礎後，你更能在團隊或合作環境中發揮領導力與影響力。

最後，「再生」或「持續更新」則是將所有這些習慣整合起來，使你能夠不斷地提升自我。一個人如果能夠定期進行身、心、智、靈四方面的更新，就能在面對生活與工作中各種挑戰時保持高度的效能與韌性。從積極主動到尋求理解，再到促進自立與互依，每個習慣都是相輔相成的，最終讓我們達到一種持續成長和再生的狀態，這正是書中所強調的核心理念。

Stephen R. Covey "The 7 Habits of Highly Effective People"

Online Dictionaries Used:

hk.dictionary.search.yahoo.com

www.oxfordlearnersdictionaries.com

Explained by Microsoft Copilot and Edited

長遠發展的不二法門

rivalry: a state in which two people, companies, etc. are competing for the same thing

politicking: political activity, especially to win support for yourself

mastermind: to plan and direct a complicated project or activity

    The writer has found that the only thrust of some organizations is to make money...We cannot live without eating, but we do not live to eat.

    如果組織只專注於金錢利益，就可能忽略其他極為重要的面向，例如員工的發展、創新、社會責任及長期可持續發展等。而我們個人層面則表達了相似的道理：雖然進食是維持生命的基本需求，但生活的意義絕非僅僅依賴於生理需求的滿足。若僅僅是「為了吃飯而活」，那就缺乏精神、情感、知識與靈性的豐富，而這正是《高效能人士的七個習慣》所提醒我們必須平衡照顧的四個面向──身體、心靈、思維與精神。

gauge: an instrument for measuring the amount or level of something

benevolent: kind, helpful and generous

autocracy: a system of government of a country in which one person has complete power

adversarial: involving people who are in opposition and who argue against each other

hallmark: ​a feature or quality that is typical of somebody/something

ascendancy: the position of having power or influence over somebody/something

Stephen R. Covey "The 7 Habits of Highly Effective People"

Online Dictionaries Used:

hk.dictionary.search.yahoo.com

www.oxfordlearnersdictionaries.com

Explained by Microsoft Copilot and Summarized

Backorder

在商業和零售領域，Backorder指的是當某商品目前缺貨時，顧客仍然可以下訂這件商品，並等待商品補貨後再進行配送。簡單來說，當庫存不足以即時供應時，商家會接受預訂，待商品重新進貨後按照順序配送給訂購者。

如果供應商庫存不足、部分商品需要Backorder，通常我司可以考慮分開兩筆交易：對於即時供貨的部分，按時付款並開票；對於Backorder的部分，則待商品實際補出後再進行單獨的開票和付款。這樣既保障了供應商的利益，也有利於我司的資金管理。

問︰當Backorder的貨品補發時，一般來說供應商會否通知我司？還是供應商會直接發貨？譬如供應商隔了很久才發貨，我司已經不需要，這樣我司便會有損失。

供應商在補發backorder貨品前通常會提前通知貴司，確認訂單仍然有效。這個通知可以透過電子郵件、訂單管理系統或專門的溝通渠道進行。提前通知讓貴司有時間評估當前需求，如果貨品補發時已不需要，可進行取消或其它調整，從而避免不必要的庫存積壓與潛在損失。

如果合同中未明確要求供應商在發貨前先通知，那供應商可能會直接發貨。

總結來說，為防範因延遲發貨而帶來的損失，最好在合作協議中約定明確的通知和確認程序。如果現有條款不夠明確，建議與供應商討論並增訂相關條款，確保雙方利益。

Microsoft Copilot and Edited

struct in C++

Basic Syntax Rules

- Case Sensitivity – C++ is case-sensitive, meaning Variable and variable are different identifiers.

- Semicolons (;) – Statements must end with a semicolon.

- Curly Braces ({}) – Used to define blocks of code, like functions or loops.

- Header Files (#include) – Used to include standard or user-defined libraries at the beginning of a program.

- Main Function (main()) – Every C++ program must have a main() function, which serves as the entry point.

In C++, std::string name; declares a variable named name of type std::string. This means name can store a sequence of characters, effectively functioning as a string.

In C++, a struct (short for structure) is a user-defined data type that groups together multiple variables of different types under a single name. It's similar to a class, but by default, its members are public instead of private.

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