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A sound wave travels through iron at a rate of
5120(m)/(s).
At what rate does the sound wave travel in
(km)/(h) ?

(km)/(h)

A sound wave travels through iron at a rate of $\frac{5120\,\text{m}}{\text{s}}$ . $\newline$ At what rate does the sound wave travel in $\frac{\text{km}}{\text{h}}$ ? $\newline$ $\square$ $\frac{\text{km}}{\text{h}}$

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Convert rates and measurements: customary units

Full solution

Q. A sound wave travels through iron at a rate of

\frac{5120\,\text{m}}{\text{s}}

.

\newline

At what rate does the sound wave travel in

\frac{\text{km}}{\text{h}}

?

\newline

\square

\frac{\text{km}}{\text{h}}

Multiply conversion factors: To convert the speed from meters per second to kilometers per hour, we need to multiply the given speed by the conversion factor from meters to kilometers and from seconds to hours. There are $1000$ meters in a kilometer and $3600$ seconds in an hour. So, the conversion factor is $(1 \, \text{km} / 1000 \, \text{m}) \times (3600 \, \text{s} / 1 \, \text{h})$ .
Calculate speed in km/h: Now, we calculate the speed in kilometers per hour by multiplying the given speed in meters per second by the conversion factor. $\newline$ Speed in $\text{km/h}$ = $5120 \, \text{m/s}$ $*$ $\left(1 \, \text{km} / 1000 \, \text{m}\right)$ $*$ $\left(3600 \, \text{s} / 1 \, \text{h}\right)$
Perform multiplication: Perform the multiplication to find the speed in kilometers per hour. $\newline$ Speed in $\text{km/h} = 5120 \times \left(\frac{1}{1000}\right) \times 3600$ $\newline$ Speed in $\text{km/h} = 5.120 \times 3600$ $\newline$ Speed in $\text{km/h} = 18432$

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