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concept

## Introduction To Sound Waves

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Hey, guys, in this video, we're gonna introduce sound waves. Now, sound is just a particular type of wave. And we've already talked a lot about waves. All right, so we're gonna apply Ah, lot of that knowledge to the specific wave of sound. Let's get to it. Sound is a common type of longitudinal wave. Okay, The oscillations that make up sound are oscillations in the pressure of gas or technically, whatever elastic, medium sound travels in sound can also travel in liquids and solids. Okay, these oscillations occur along the propagation direction, which means that it has to be a longitudinal wave. Here is a very, very common picture of sound. We have some sort of source, like a speaker producing sound. What it causes is it causes areas of compression of the medium. You can see a high density of gas molecules right here, and then it causes areas of rare faction which is a decrease in the density. Okay. And then you see another area of compression here and then mawr Rare faction here. Okay. And what happens is as the gaskets denser and denser and denser, the pressure goes up. So if I were to plot pressure versus distance here, you would see that it starts at the highest pressure. We have a very, very dense area right here. Then it steadily decreases to an area of low pressure. Then it steadily increases back to another area of maximum pressure before ending at an area of low pressure. So this is what the pressure as a function of position would look like. All right. Now, remember, all of the same rules apply toe longitudinal waves. All the same rules apply the longitudinal waves that apply to trans verse waves. The speed relation they all have amplitude is that they have periods. They have frequencies, etcetera. The thing unique to each type of wave is the energy that it carries and, more importantly, the speed. So we're gonna talk a little bit about the speed here. Specifically the speed of sound in an ideal gas. This is equal to the square root of gamma R t over em. Okay, where are is the ideal constant, which is 8.3 Jules per mole. Kelvin, that's an S I units and gamma is a constant called the heat capacity ratio. Okay, remember, guys, or if you haven't learned it yet you will see it soon that the heat capacity given by the Capital C is a measure of how much heat is needed to change the temperature of a substance. Now, since this doesn't cover really thermodynamics, the section is not dealing with their own dynamics. The heat capacity ratio won't really be addressed too much. But this is just what it iss there happened to be to heat capacities that exists for gas is the heat capacity at constant pressure and the heat capacity at constant volume. The ratio is, as it sounds, just the ratio of those two heat capacities. Okay, Now, the speed of sound for an air is a very, very common formula given in this orange box where T is in units of degrees Celsius. This tea is in units of Kelvin. Okay, Whenever you have t typically in an equation, it's going to be in Kelvin. But this specific one for the speed of sound is an outlier. It's written so that t is in units of Celsius. Okay, let's do an example to wrap this up. What is the heat capacity ratio for air? Consider air toe. Have a Moeller mass of 2.88 times 10 to the negative. 2 kg per mole. Now, because temperature appears in the both speed equations, right, we have that. The speed of sound is specifically 3 31 meters per second times the square root of one plus t over to 73. And it appears in gamma r t over em. Okay, those teas, they're gonna balance out so we can actually choose whatever temperature we want. Okay, I'm gonna choose a temperature of zero degrees Celsius, which equals 273 Calvin. Okay. If I plug in zero here, then this is just 3. 31. And this equals the square to gamma. Our teeth over capital M capital in is the molar mass. And we're told that the Moller massive air is considered to be this. So all I have to do now is do 3. 31 squared equals gamma r t over em. And so gamma is m 3 squared over rt. And so gamma Oh, sorry that minimize yourself so you can see that equation m 3 31 squared over r t. So gamma is just to times 10 to the negative too. 3. 31 That squared those air. Both in S I units already our was given an S I units 8.3 temperature and s I units is to 73 this works out to 1.4. And if you were to look up the heat capacity ratio for air, you would indeed find that it is 1.4. Alright, guys, that wraps up this introduction into sound waves. Thanks for watching.

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Problem

A sound wave is emitted at a frequency of 300 Hz in air at a 0°C. As the sound wave travels through the air, the temperature increases. What is the wavelength of the sound wave at the following temperatures?

a. 0°C

b. 20°C

c. 45°C

A

(a) λ=1.10 m; (b) λ=1.14 m; (c) 1.19 m

B

(a) λ=1.10 m; (b) λ=1.14 m; (c) 1.29 m

C

(a) λ=1.10 m; (b) λ=1.18 m; (c) 1.19 m

D

(a) λ=1.10 m; (b) λ=1.18 m; (c) 1.29 m

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concept

## Sound Waves In Liquids And Solids

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Hey guys, we already saw the speed of sound in an ideal gas. Now we want to talk about the speed of sound specifically in liquids and solids, which are also elastic media, so they can also propagate sound waves. All right, let's get to it. As I said, sound can travel through any elastic medium, so we could also travel in liquids and solids. Alright, sound travel through a solid or liquid would look the same to sound. Traveling through gas. It would just have a different speed. Okay, the speed of sound in a liquid is equal to the square root of be divided by row, where B is known as the bulk module lists of the liquid and row is just the plain old density, the speed of sound in a thin solid. So something like a rod. If you were to put a little speaker with sound thing that sound propagated on the thin solid is gonna be the square root of why over row, where Roe is still just the plain old density, and why is known as the young's modu Elice of the solid. Okay, now, if you've covered elastic elasticity, then you've seen ma July before, If not what? A module ISS is of a solid or liquid is it's a measure of the elasticity of that substance. Okay, the larger the module iss, the harder it is to compress that material. Okay, so if you want to take a chunk of something and you want to squeeze it from all sides to a smaller chunk of that something, the larger the bulk module lists the mawr Force, you're gonna have to put on every surface. The more pressure you're gonna have to put on all the surfaces. Thio get it to change its volume. Okay for the young's modu Elice. If you have a rod, the larger the Youngs modulates, the harder you're gonna press on the end of the rod to reduce its length. Okay, the more pressure you're gonna have to apply on the end of the rod to reduce its length. Let's do an example. De ionized water has a bulk module list of 22 times 10 to the nine Pascal's. What is the wavelength of a 250 hertz sound wave in D I water? Okay, if we want to know the wavelength of some frequency we know that the speed relates the two. Okay, What's the speed of sound In de ionized water. Well, the speed is gonna be the bulk module ists divided by the density. The bulk modulates were told and the density of the water is just kg per cubic meter. But right, that's an S I units. And this whole thing is going to be 14 meters per 2nd 1483 m per second. So with wavelength is gonna be 83 divided by 250 hertz, which is 5.93 m of pretty large wavelength. But that's because sound is traveling so quickly. Okay, so it travels such a far such a far distance per unit time. Alright, guys, that wraps up our little discussion here on the speed of sound in liquids and solids. Thanks for watching

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