Physics Examples

$λ = \frac{v}{f}$

$λ$	$=$	$?$
$v$	$=$	$3.6 \cdot 10^{2} \frac{m}{s}$
$f$	$=$	$1.2 \cdot 10^{3} Hz$

Step 1

Substitute the given values into $λ = \frac{v}{f}$ .

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Step 1.1

Substitute $3.6 \cdot 10^{2} \frac{m}{s}$ for $v$ .

$λ = \frac{3.6 \cdot 10^{2} \frac{m}{s}}{f}$

Step 1.2

Substitute $1.2 \cdot 10^{3} Hz$ for $f$ .

$λ = \frac{3.6 \cdot 10^{2} \frac{m}{s}}{1.2 \cdot 10^{3} Hz}$

$λ = \frac{3.60 \cdot 10^{2} \frac{m}{s}}{1.20 \cdot 10^{3} Hz}$

Step 2

Simplify the right side.

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Step 2.1

Cancel the common factor of $10^{2}$ and $10^{3}$ .

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Step 2.1.1

Factor $10^{2}$ out of $3.60 \cdot 10^{2} \frac{m}{s}$ .

$λ = \frac{10^{2} (3.60 \frac{m}{s})}{1.20 \cdot 10^{3} Hz}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $10^{2}$ out of $1.20 \cdot 10^{3} Hz$ .

$λ = \frac{10^{2} (3.60 \frac{m}{s})}{10^{2} (1.20 \cdot 10 Hz)}$

Step 2.1.2.2

Cancel the common factor.

$λ = \frac{10^{2} (3.60 \frac{m}{s})}{10^{2} (1.20 \cdot 10 Hz)}$

Step 2.1.2.3

Rewrite the expression.

$λ = \frac{3.60 \frac{m}{s}}{1.20 \cdot 10 Hz}$

Step 2.2

Multiply $1.20$ by $10$ .

$λ = \frac{3.60 \frac{m}{s}}{12.00 Hz}$

Step 2.3

Rewrite $Hz$ as $\frac{1}{s}$ .

$λ = \frac{3.60 \frac{m}{s}}{12.00 \frac{1}{s}}$

Step 2.4

Factor $\frac{m}{s}$ out of $\frac{3.60 \frac{m}{s}}{12.00 \frac{1}{s}}$ .

$λ = \frac{m}{s} \cdot \frac{3.60}{12.00 \frac{1}{s}}$

Step 2.5

Combine fractions.

$λ = \frac{3.60}{12.00} \frac{m}{\frac{s}{s}}$

Step 2.6

Divide $3.60$ by $12.00$ .

$λ = 0.3 \frac{m}{\frac{s}{s}}$

Step 2.7

Cancel $s$ .

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Step 2.7.1

Cancel $s$ .

$λ = 0.3 \frac{m}{\frac{s}{s}}$

Step 2.7.2

Rewrite the expression.

$λ = 0.3 \frac{m}{1}$

Step 2.8

Cancel $m$ .

$λ = 0.3 \frac{m}{1}$

Step 2.9

Rewrite the expression.

$λ = 0.3 m$

Step 3

Round to $3$ significant figures.

$λ = 0.300 m$

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