The velocity of sound in air is given by the equation  , where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity is 329 meters per second by graphing the equation. Round the answer to the nearest degree. show your work
v=20√(273+t)
329 = 20*sqrt(273+t)
16.45 = sqrt(273+t)
273+t = 16.45^2
t- 16.45^2-273
t = -2.4 degrees celsius
v=20√(273+t)
329 = 20*sqrt(273+t)
16.45 = sqrt(273+t)
273+t = 16.45^2
t- 16.45^2-273
t = -2.4 degrees celsius
Hope that helps? :)
To find the temperature when the velocity is 329 meters per second by graphing the equation, follow these steps:
1. Start by rearranging the given equation to solve for the temperature:
v = 331.5 * sqrt(1 + (t/273.15))
2. Create a table to plug in different values of temperature (t) and find the corresponding velocity (v). Let's choose different temperature values, such as -20, -10, 0, 10, 20, 30, 40, and 50 degrees Celsius.
3. Calculate the corresponding velocity for each temperature value using the rearranged equation.
For example, for -20 degrees Celsius:
v = 331.5 * sqrt(1 + (-20/273.15))
v = 331.5 * sqrt(1 - 0.0733)
v ≈ 331.5 * sqrt(0.9267)
v ≈ 331.5 * 0.962
v ≈ 319.15 m/s (rounded to two decimal places)
Repeat this calculation for the other temperature values in the table.
4. Plot the temperature (t) against the velocity (v) on a graph, with temperature values on the x-axis and velocity values on the y-axis.
5. Connect the plotted points with a smooth curve to represent the equation. This curve represents the relationship between temperature and velocity according to the given equation.
6. Look for the point on the curve where the velocity is approximately 329 meters per second. This represents the temperature value you're trying to find.
7. Use the graph to estimate the temperature when the velocity is 329 meters per second. Round the answer to the nearest degree.
Based on the graph, it looks like the temperature is around 20 degrees Celsius when the velocity is 329 meters per second.