What is the speed of sound in air (a) on a cold winter day in Minnesota when the temperature is -25°F, and (b) on a hot summer day in Death Valley when the temperature is 125°F?

Video transcript

Hey, everyone in this problem, we're asked to determine the velocity of sound. OK? And for part one on the deck of a ship in the ocean at negative 10 degrees Celsius. And for part two inside the heater room on the ship where the temperature is degrees Celsius, we're given four answer choices A through D and each of them just have a different combination of that velocity for the two cases. So we're looking for the velocity of sound. Thanks giving some temperature. So let's recall that we can write that the velocity of sound for the speed of sound is equal to m per second multiplied by the square root of T plus 273 divided by 273. Now, when I write the equation like this, the temperature K is in degrees Celsius, you may have seen this equation where you multiply by just the square root of T divided by 273. That's the exact same equation. But in that case, the temperatures in Kelvin, OK. So in this one, by adding 273 we convert our Celsius to Kelvin. OK. So it's the exact thing we were given degrees Celsius, which is why I've written it like this. All right. So we have our equation. The only thing we need to know is the temperature in order to substitute it in and solve for the speed of sound. We have those temperatures. So we're gonna just get started on part one by substituting in our temperature of negative 10 degrees Celsius. We have that V S is gonna be equal to m per second. Multiplied by the square root of negative plus 273 divided by 273. We can simplify. This is gonna be 331 m per second multiplied by the square root of 263 divided by 273 which is equal to 324. m per second. One thing I wanna point out here in this square root, this ratio of temperatures, you can see that because we had a negative temperature in the numerator for the Celsius degrees Celsius, OK. The numerator ended up being less than 273. That makes this ratio less than one because the numerator is less than the denominator. So this ratio is less than one when you multiply by something that's less than one, you're gonna get a smaller value, ok? When that temperature is negative, it's going to decrease the numerator. We're gonna have this ratio that's less than one and this speed is gonna become smaller and slower. So speed of sound at negative 10 degrees Celsius is gonna be 324.88 m per second. And if we do the same for part two and the speed of sound is gonna be equal to 331 meters per second, Multiplied by the square root of 30 plus 273 divided by 273. Hey, this time we're, we have positive 30. So we get 331 m per second, multiplied by the square root of 303 divided by 273. And you can see that 303 is bigger. Now, the numerator is bigger, this fraction is gonna be greater than one. So we're gonna be multiplying by something that's greater than one. We're gonna get a higher speed, ok? And if we work it out, we get that, it's equal to 0.713 m per second. All right. So our choices are rounded to the nearest meter per second. So for the negative 10 degrees on the deck rounding to the nearest meter per second, we get that. The speed of sound is 325 m per second. And for part two in the heater room at 30 degrees Celsius. The speed of sound is 349 m per second. This corresponds with answer choice A that's it for this one. Thanks everyone for watching. See you in the next video.