Physics Examples

$λ = \frac{v}{f}$

$λ$	$=$	$?$
$v$	$=$	$7.2 \cdot 10^{3} \frac{m}{s}$
$f$	$=$	$1028.57 Hz$

Step 1

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

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Step 1.1

Substitute $7.2 \cdot 10^{3} \frac{m}{s}$ for $v$ .

$λ = \frac{7.2 \cdot 10^{3} \frac{m}{s}}{f}$

Step 1.2

Substitute $1028.57 Hz$ for $f$ .

$λ = \frac{7.2 \cdot 10^{3} \frac{m}{s}}{1028.57 Hz}$

$λ = \frac{7.20 \cdot 10^{3} \frac{m}{s}}{1028.57 Hz}$

Step 2

Simplify the right side.

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Step 2.1

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

$λ = \frac{7.20 \cdot 10^{3} \frac{m}{s}}{1028.57 \frac{1}{s}}$

Step 2.2

Factor $\frac{m}{s}$ out of $\frac{7.20 \cdot 10^{3} \frac{m}{s}}{1028.57 \frac{1}{s}}$ .

$λ = \frac{m}{s} \cdot \frac{7.20 \cdot 10^{3}}{1028.57 \frac{1}{s}}$

Step 2.3

Combine fractions.

$λ = \frac{7.20 \cdot 10^{3}}{1028.57} \frac{m}{\frac{s}{s}}$

Step 2.4

Divide using scientific notation.

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Step 2.4.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$λ = (\frac{7.20}{1028.57}) (\frac{10^{3}}{1}) \frac{m}{\frac{s}{s}}$

Step 2.4.2

Divide $7.20$ by $1028.57$ .

$λ = 0.00700000 \frac{10^{3}}{1} \frac{m}{\frac{s}{s}}$

Step 2.4.3

Divide $10^{3}$ by $1$ .

$λ = 0.00700000 \cdot 10^{3} \frac{m}{\frac{s}{s}}$

Step 2.5

Move the decimal point in $0.00700000$ to the right by $3$ places and decrease the power of $10^{3}$ by $3$ .

$λ = 7.00000972 \cdot 10^{0} \frac{m}{\frac{s}{s}}$

Step 2.6

Convert $7.00000972 \cdot 10^{0}$ from scientific notation.

$λ = 7.00000972 \frac{m}{\frac{s}{s}}$

Step 2.7

Cancel $s$ .

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Step 2.7.1

Cancel $s$ .

$λ = 7.00000972 \frac{m}{\frac{s}{s}}$

Step 2.7.2

Rewrite the expression.

$λ = 7.00000972 \frac{m}{1}$

Step 2.8

Cancel $m$ .

$λ = 7.00000972 \frac{m}{1}$

Step 2.9

Rewrite the expression.

$λ = 7.00000972 m$

Step 3

Round to $3$ significant figures.

$λ = 7.00 m$

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