# Question 20441

Jul 21, 2017

Because they are too big to be quantum mechanical.

An object with mass $m$ that moves at some speed $v$ has a wavelength $\lambda$ according to the de Broglie Relation:

$\lambda = \frac{h}{m v}$

where $h = 6.626 \times {10}^{- 34} \text{J"cdot"s}$ is Planck's constant.

Say a cricket ball was moving at an ordinary speed of $\text{90 mph}$, or $\text{40.2336 m/s}$. The average mass of a cricket ball is about $\text{5.5 oz}$, or about $\text{0.1559 kg}$.

So, the wavelength of a typical cricket ball is:

$\textcolor{b l u e}{\lambda} = \left(6.626 \times {10}^{- 34} \cancel{\text{kg"cdot"m"^cancel(2)"/s")/(0.1559 cancel"kg" xx 40.2336 cancel"m/s}}\right)$

$= 1.056 \times {10}^{- 34} \text{m}$,

or

$= \textcolor{b l u e}{1.056 \times {10}^{- 25} \text{nm}}$.

In the EM spectrum, gamma rays have the lowest wavelength on the order of ${10}^{- 3} \text{nm}$ (and the highest energy).

So, cricket balls have much, much shorter wavelengths (and thus much, much higher frequencies) than we can observe. It is literally outside the EM spectrum.

We say then that they have no observable wave properties.

In analogy with sound, human beings can only perceive down to about $\text{20 Hz}$ (sub bass frequencies), or sound with a wavelength of

["20 s"^(-1) / (34300 "cm/s")]^(-1) = "1715 cm"#

which is shorter wavelength than AM but longer than FM radio.

We physically can't hear frequencies lower than that, and thus we physically can't hear wavelengths above $\text{1715 cm}$.

Similarly, we cannot perceive the low wavelengths, or high frequencies, of cricket balls and big objects like that, because they are too high.