Physics Examples

$λ = \frac{v}{f}$

$λ$	$=$	$7 m$
$v$	$=$	$7.2 \cdot 10^{3} \frac{m}{s}$
$f$	$=$	$?$

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 $7 m$ for $λ$ .

$f = \frac{v}{7 m}$

Step 2.2

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

$f = \frac{7.2 \cdot 10^{3} \frac{m}{s}}{7 m}$

$f = \frac{7.20 \cdot 10^{3} \frac{m}{s}}{7.00 m}$

Step 3

Simplify the right side.

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Step 3.1

Factor $\frac{m}{s}$ out of $\frac{7.20 \cdot 10^{3} \frac{m}{s}}{7.00 m}$ .

$f = \frac{m}{s} \cdot \frac{7.20 \cdot 10^{3}}{7.00 m}$

Step 3.2

Cross cancel units.

$f = \frac{m}{s} \cdot \frac{7.20 \cdot 10^{3}}{7.00 m}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Remove the canceled units.

$f = \frac{1}{s} \cdot \frac{7.20 \cdot 10^{3}}{7.00}$

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.

$f = \frac{1}{s} ((\frac{7.20}{7.00}) (\frac{10^{3}}{1}))$

Step 3.3.2.2

Divide $7.20$ by $7.00$ .

$f = \frac{1}{s} (1.02857142 \frac{10^{3}}{1})$

Step 3.3.2.3

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

$f = \frac{1}{s} \cdot 1.02857142 \cdot 10^{3}$

Step 3.3.3

Combine $\frac{1}{s}$ and $1.02857142 \cdot 10^{3}$ .

$f = 1.02857142 \cdot 10^{3} \frac{1}{s}$

Step 3.3.4

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

$f = 1.02857142 \cdot 10^{3} Hz$

Step 3.3.5

Convert $1.02857142 \cdot 10^{3}$ to decimal.

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Step 3.3.5.1

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

$f = 1.02857142 \cdot 1000 Hz$

Step 3.3.5.2

Multiply $1.02857142$ by $1000$ .

$f = 1028.57142857 Hz$

Step 4

Round to $3$ significant figures.

$f = 1.03 \cdot 10^{3} Hz$

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