A sound wave in a particular object
has a frequency of 260 hertz and a wavelength of 2.5 meters. At what speed does the sound wave
propagate in that object to the nearest meter per second?
Let’s begin by writing down the
values that we’ve been given here. We already know that the object has
a frequency represented by 𝑓 of 260 hertz and a wavelength 𝜆 of 2.5 meters. Now to answer this question, recall
that we can relate the frequency and wavelength of a wave to its speed 𝑠 using the
formula 𝑠 equals 𝑓 times 𝜆. Since we already have values for
both of the terms on the right-hand side of the formula, let’s go ahead and
substitute them in. Frequency times wavelength gives us
260 hertz times 2.5 meters. But before we calculate, let’s take
a moment to think about the units here.
Recall that hertz has base SI units
of inverse seconds. And if we choose to write our
frequency value like this, it’s easier to see how this formula combines units of per
seconds with units of meters to give us a final value in meters per second, which is
a good sign because we are solving for a speed. All that’s left to do now is
calculate. And 260 times 2.5 comes out to
exactly 650. This value is already written to
the nearest meter per second, so we have our answer. The sound wave in this object
travels at a speed of 650 meters per second.