What does it mean when we say that wavelength is inversely proportional to frequency?

When we say that wavelength is inversely proportional to frequency, we are referring to the relationship between the two properties of a wave, particularly when the wave is moving at a constant speed. This relationship is described by the wave equation, which states that the product of the wavelength (λ) and the frequency (f) of a wave is equal to the speed (v) of the wave: v = λ * f In this equation, if the speed of the wave is constant (as it is for a given medium like air or water), then as the frequency increases, the wavelength must decrease to keep the product the same, and vice versa. This is the essence of being "inversely proportional." So, when we say that wavelength and frequency are inversely proportional, we mean that as one increases, the other decreases in such a way that their product remains constant for a wave traveling at a fixed speed. Now, let's translate that into Chinese: 当我们说波长与频率成反比时，我们指的是波的两个属性之间的关系，特别是当波以恒定速度移动时。这种关系由波动方程描述，该方程表明波的波长（λ）和频率（f）的乘积等于波的速度（v）： v = λ * f 在这个方程中，如果波的速度是恒定的（就像在空气或水这样的介质中一样），那么随着频率的增加，波长必须减少以保持乘积不变，反之亦然。这就是“成反比”的本质。 所以，当我们说波长和频率成反比时，我们的意思是，随着一个的增加，另一个会以这样的方式减少，使得它们对于以固定速度传播的波的乘积保持不变。

The concept can also be applied to periodic waves of non-sinusoidal shape. ... Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.