A sound wave in a particular object propagates at 4670 meters per second and has a wavelength of 0.75 meters. What is the frequency of the sound wave, to the nearest hertz?
Okay, so in this question, we’re being told that we have a particular object. So let’s say that this here is a particular object. And we’ve also been told that there are sound waves propagating through the subject. So let’s say that these are our sound waves propagating left to right. Now, we’ve been told that the velocity of the sound waves in the subject is 4670 meters per second. And we’ll call this velocity 𝑣. Additionally, we’ve also been told the wavelength of the sound waves. So we can say that the wavelength which we will call 𝜆 is equal to 0.75 meters.
Based on this information, we need to find the frequency of the sound wave to the nearest hertz. To do this, we need to recall the following relationship: 𝑣 — the speed of sound in a particular object — is equal to the frequency of the sound wave in that object multiplied by the wavelength of the sound wave. And in this equation, we already know the velocity of the sound wave and the wavelength. And we’re being asked to calculate the frequency. So we can do this simply by rearranging our equation. If we divide both sides by the wavelength 𝜆, then we see that it cancels on the right-hand side. And what we’re left with is that the speed of sound in this object divided by the wavelength is equal to the frequency.
Additionally, we can see that the quantities we’ve been given — the velocity of the sound wave and its wavelength — have been given in their base units, meters per second for velocity and meters for wavelength. Therefore, when we calculate the frequency, we will find it in its own base unit. And the base unit for frequency we can recall is the hertz. So let’s go back finding this frequency.
We can say that the frequency is equal to the speed of the sound wave divided by the wavelength of the sound wave. And when we evaluate the fraction on the right-hand side, we find that the frequency is equal to 6226.6 recurring hertz. But we’ve been asked to give our answer to the nearest hertz. So we need to round this value here. To do this, we look at the value after it. This value is a six. And six is greater than five. Therefore, this number here is going to round up.
And so, our final answer is that the frequency of the sound wave is 6227 hertz to the nearest hertz.