A sound wave in a particular object propagates at 960 metres per second and has a frequency of 800 hertz. What is the wavelength of the sound wave in that object?
Okay, so in this question, we’re being given information about the speed of sound in a particular object. So let’s say that this is the object that we’ve been given information about. And we’ve been told that sound waves are travelling in this object at 960 metres per second. Additionally, we’ve been told that the frequency of these particular sound waves is 8000 hertz or, in other words, 8000 cycles every second. And based on this information, we need to work out the wavelength of these sound waves.
Now to do this, we need to recall the relationship between sound speed, frequency, and wavelength. The relationship that we’re looking for is this one. The sound speed, which we call 𝑣, is equal to the frequency of the sound waves multiplied by the wavelength of the sound waves. Now it’s worth noting here that 𝑣, the speed of sound, changes depending on the material in which the sound is travelling. And that’s why the question specifies for us that the speed of sound in this particular object is 960 metres per second.
But anyway, so if we want to find the answer to our question here, we need to use this equation. And more specifically, we need to rearrange it to solve for the wavelength. To do this, we need to isolate 𝜆, the wavelength on one side of the equation. And this can be done by dividing both sides of the equation by the frequency 𝑓 because this way, on the right-hand side, the frequency cancels and what we’re left with is that 𝑣 over 𝑓 is equal to 𝜆. Or in other words, the speed of sound in this material divided by the frequency of this particular sound wave is equal to the wavelength of this particular sound wave.
At this point then we can plug in some numbers. We can say that the wavelength 𝜆 is equal to 960 metres per second, that’s the sound speed, divided by 8000 hertz, that’s the frequency of the sound wave. And at this point, we can realise that both of the quantities given to us on the right-hand side of this equation are in their base units because the base unit of speed is metres per second, and the base unit of frequency is hertz. And remember a hertz in frequency is equivalent to one cycle per second.
But anyway, so because we’ve got base units in both the quantities on the right-hand side of our equation, this means that when you calculate this right-hand side fraction, our answer will be in the base unit of wavelength. And remember, wavelength is indeed a length and so the base unit of wavelength is metres. Therefore, our final answer is going to be 960 divided by 8000 metres. And so at this point, we found the answer to our question. The wavelength of the sound wave in this particular object is 0.12 metres.