Physics Examples

$λ = \frac{v}{f}$

$λ$	$=$	$0.3 m$
$v$	$=$	$3.6 \cdot 10^{2} \frac{m}{s}$
$f$	$=$	$?$

Step 1

Solve for $f$ .

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Step 1.1

Rewrite the equation as $\frac{v}{f} = λ$ .

$\frac{v}{f} = λ$

Step 1.2

Find the LCD of the terms in the equation.

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Step 1.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$f, 1$

Step 1.2.2

The LCM of one and any expression is the expression.

$f$

Step 1.3

Multiply each term in $\frac{v}{f} = λ$ by $f$ to eliminate the fractions.

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Step 1.3.1

Multiply each term in $\frac{v}{f} = λ$ by $f$ .

$\frac{v}{f} f = λ f$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $f$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{v}{f} f = λ f$

Step 1.3.2.1.2

Rewrite the expression.

$v = λ f$

Step 1.4

Solve the equation.

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Step 1.4.1

Rewrite the equation as $λ f = v$ .

$λ f = v$

Step 1.4.2

Divide each term in $λ f = v$ by $λ$ and simplify.

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Step 1.4.2.1

Divide each term in $λ f = v$ by $λ$ .

$\frac{λ f}{λ} = \frac{v}{λ}$

Step 1.4.2.2

Simplify the left side.

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Step 1.4.2.2.1

Cancel the common factor of $λ$ .

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Step 1.4.2.2.1.1

Cancel the common factor.

$\frac{λ f}{λ} = \frac{v}{λ}$

Step 1.4.2.2.1.2

Divide $f$ by $1$ .

$f = \frac{v}{λ}$

Step 2

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

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Step 2.1

Substitute $0.3 m$ for $λ$ .

$f = \frac{v}{0.3 m}$

Step 2.2

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

$f = \frac{3.6 \cdot 10^{2} \frac{m}{s}}{0.3 m}$

$f = \frac{3.60 \cdot 10^{2} \frac{m}{s}}{0.300 m}$

Step 3

Simplify the right side.

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Step 3.1

Factor $\frac{m}{s}$ out of $\frac{3.60 \cdot 10^{2} \frac{m}{s}}{0.300 m}$ .

$f = \frac{m}{s} \cdot \frac{3.60 \cdot 10^{2}}{0.300 m}$

Step 3.2

Cross cancel units.

$f = \frac{m}{s} \cdot \frac{3.60 \cdot 10^{2}}{0.300 m}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Remove the canceled units.

$f = \frac{1}{s} \cdot \frac{3.60 \cdot 10^{2}}{0.300}$

Step 3.3.2

Divide using scientific notation.

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Step 3.3.2.1

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

$f = \frac{1}{s} ((\frac{3.60}{0.300}) (\frac{10^{2}}{1}))$

Step 3.3.2.2

Divide $3.60$ by $0.300$ .

$f = \frac{1}{s} (12 \frac{10^{2}}{1})$

Step 3.3.2.3

Divide $10^{2}$ by $1$ .

$f = \frac{1}{s} \cdot 12 \cdot 10^{2}$

Step 3.3.3

Combine $\frac{1}{s}$ and $12 \cdot 10^{2}$ .

$f = 12 \cdot 10^{2} \frac{1}{s}$

Step 3.3.4

Move the decimal point in $12$ to the left by $1$ place and increase the power of $10^{2}$ by $1$ .

$f = 1.2 \cdot 10^{3} \frac{1}{s}$

Step 3.3.5

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

$f = 1.2 \cdot 10^{3} Hz$

Step 3.3.6

Convert $1.2 \cdot 10^{3}$ to decimal.

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Step 3.3.6.1

Raise $10$ to the power of $3$ .

$f = 1.2 \cdot 1000 Hz$

Step 3.3.6.2

Multiply $1.2$ by $1000$ .

$f = 1200.0 Hz$

Step 4

Round to $3$ significant figures.

$f = 1.20 \cdot 10^{3} Hz$

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