Physics Examples

λ = \frac{v}{f}

$λ = \frac{v}{f}$

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

Step 1

Substitute the given values into

λ = \frac{v}{f}

$λ = \frac{v}{f}$ .

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Step 1.1

Substitute

7.2 \cdot 10^{3} \frac{m}{s}

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

v

$v$ .

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

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

Step 1.2

Substitute

1028.57 Hz

$1028.57 Hz$ for

f

$f$ .

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

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

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

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

Step 2

Simplify the right side.

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Step 2.1

Rewrite

Hz

$Hz$ as

\frac{1}{s}

$\frac{1}{s}$ .

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

$\frac{m}{s}$ out of

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

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

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

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

Step 2.3

Combine fractions.

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

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

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}}

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

Step 2.4.2

Divide

7.20

$7.20$ by

1028.57

$1028.57$ .

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

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

Step 2.4.3

Divide

10^{3}

$10^{3}$ by

1

$1$ .

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

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

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

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

Step 2.5

Move the decimal point in

0.00700000

$0.00700000$ to the right by

3

$3$ places and decrease the power of

10^{3}

$10^{3}$ by

3

$3$ .

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

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

Step 2.6

Convert

7.00000972 \cdot 10^{0}

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

λ = 7.00000972 \frac{m}{\frac{s}{s}}

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

Step 2.7

Cancel

s

$s$ .

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Step 2.7.1

Cancel

s

$s$ .

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

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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