From 56333b2451b015a09bc044b0d68b2450fe2e1432 Mon Sep 17 00:00:00 2001 From: che0815 Date: Sun, 22 Feb 2026 09:16:24 +0100 Subject: [PATCH] feature: new solution for AA116 --- contents/solutions/AA116.md | 9 +++++++++ 1 file changed, 9 insertions(+) create mode 100644 contents/solutions/AA116.md diff --git a/contents/solutions/AA116.md b/contents/solutions/AA116.md new file mode 100644 index 0000000..1de0114 --- /dev/null +++ b/contents/solutions/AA116.md @@ -0,0 +1,9 @@ +# Gegeben +* Sendefrequenz: $\qty{14,2}{\mega\hertz}$ +* Genauigkeit: $\qty{10}{\ppm}$ + +# Lösungsweg +$\unit{ppm}$ steht für *parts per million*, $\qty{10}{\ppm}$ bedeutet also also $10$ pro $10^6$. +Die tatsächliche Sendefrequenz befindet sich zwischen $f_\text{min}$ und $f_\text{max}$. +$f_\text{min} = f - 10 \cdot \frac{f}{10^6} = \qty{14,2}{\mega\hertz} - 10 \cdot \frac{14,2\cdot \qty{\cancel{10^6}}{\mega\hertz}}{\cancel{10^6}} = \qty{14,2}{\mega\hertz} - \qty{142}{\hertz} = \qty{14,199858}{\mega\hertz}$ +$f_\text{max} = f + 10 \cdot \frac{f}{10^6} = \qty{14,2}{\mega\hertz} + 10 \cdot \frac{14,2\cdot \qty{\cancel{10^6}}{\mega\hertz}}{\cancel{10^6}} = \qty{14,2}{\mega\hertz} + \qty{142}{\hertz} = \qty{14,200142}{\mega\hertz}$ \ No newline at end of file