The speed of sound in air at 20°C is 344 m/s. (a) What is the wav...

Question

The speed of sound in air at 20°C is 344 m/s. (a) What is the wavelength of a sound wave with a frequency of 784 Hz, corresponding to the note G5 on a piano, and how many milliseconds does each vibration take? (b) What is the wavelength of a sound wave one octave higher (twice the frequency) than the note in part (a)?

Accepted Answer

Hey everyone in this problem, we have room temperatures defined as 25°C. The speed of sound at room temperature we're told is 346 m/s. An engineer is using a sound wave with a frequency of 1000 hertz to tune the sound level in a piece of equipment. Were asked to determine the wavelength and time for one oscillation in milliseconds and to determine the new wavelength, if the frequency is quadrupled. Alright, so let's start with part one. And we're asked to find the wavelength and let's recall that the wavelength lambda is going to be equal to the speed V over the frequency F. And those are both quantities we were given in the problem, we were given that the speed of sound is 346 m per second and that the frequency is 1000 hertz. So using those two values, we get that the wavelength is going to be 346 m per second divided by 1000 hertz. Which gives us a weight length of 0.346 m. So that's the first part of that first question. The second thing we're asked to do is find the time for one oscillation in milliseconds now were called at the time for one oscillation. Well, that's the period. We give that a special name and that is the period and it is denoted by T. So what we want to do is find the period. T. Now recall that the period is related to the inverse of the frequency. So the period T is inversely related to frequency. We have that the period is equal to one over the frequency F. Were given a frequency of 1000 hertz. And so our period is going to be one over 1000 hertz Which is equal to 0. seconds. Now the question asked us to find this in terms of milliseconds instead of seconds. So in order to go from seconds to milliseconds we're going to multiply recall that there are milliseconds per second. So we multiply by 1000 the unit of second cancels and we're left with one millisecond. And so for part one we found a wavelength of 10. m and we found a period of one millisecond. If we were looking at our answer traces we would see that the only one that corresponds to these two values is be. But let's do a part two and just verify that that answer is correct as well and see how to approach that problem. So part two is asking us to determine the new wavelength if the frequency is quadrupled. Okay so part two we want to find the new wavelength we'll call it lambda Nu if the frequency is tripled. So in order to find the new wave length we're gonna have this speed over the new frequency. Now the speed stays the same. It's V. The new frequency has been quadrupled. So it's gonna be four times our original frequency F. This gives us 346 m/s, Divided by 4000 Hz. Which gives a new wavelength of 0. 865 m. And that is going to be that new wavelength. And what you'll notice is that when we quadrupled the frequency, when we multiplied the frequency by four, the wavelength was reduced four times. Okay, so multiply the frequency by four and the wavelength was divided by four. Okay, so those two are inversely related. Alright? So if we go back up to our inter choices, We found that the wavelength was 0. m. The time for one oscillation was one millisecond. And the new wavelength, if we quadrupled, the frequency was 0.0865 m. And so we have answer choice b. Thanks everyone for watching. I hope this video helped see you in the next one.

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