From b294fba2693446bbe9d4fe754f3a9e3bbf890330 Mon Sep 17 00:00:00 2001 From: che0815 Date: Mon, 23 Feb 2026 19:45:13 +0100 Subject: [PATCH] feature: new solution for AI509 --- contents/solutions/AI509.md | 11 +++++++++++ 1 file changed, 11 insertions(+) create mode 100644 contents/solutions/AI509.md diff --git a/contents/solutions/AI509.md b/contents/solutions/AI509.md new file mode 100644 index 0000000..a6f2bea --- /dev/null +++ b/contents/solutions/AI509.md @@ -0,0 +1,11 @@ +# Gegeben +* Messwert: $f = \qty{145}{\mega\hertz}$ +* Genauigkeit: $\qty{10}{\ppm}$ + +# Lösungsweg +$\unit{ppm}$ steht für *parts per million*, $\qty{10}{\ppm}$ bedeutet also $10$ pro $10^6$. + +$\Delta f = \qty{145}{\mega\hertz} \cdot \frac{10}{10^6} = 145\cdot \cancel{10^6}\unit{\hertz}\cdot\frac{10}{\cancel{10^6}} = \qty{1450}{\hertz}$ + +$f_\text{min} = f - \Delta f = \qty{145}{\mega\hertz} - \qty{1450}{\mega\hertz} = \qty{144,99855}{\mega\hertz}$ +$f_\text{max} = f + \Delta f = \qty{145}{\mega\hertz} + \qty{1450}{\mega\hertz} = \qty{145,00145}{\mega\hertz}$ \ No newline at end of file