Consider a pipe with a length of 57.5 cm. If the temperature of the air is 21.5degrees C and the pipe is closed in one end and open in the other, what is the frequency of the third harmonic for the pipe? Post your answer in hertz (Hz) and with 3 significant figures.
http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/souspe.html
frequency closed end pipe
remember wavelength = speed of sound * T = speed of sound / f
and then
http://www.physicsclassroom.com/class/sound/Lesson-5/Open-End-Air-Columns
To determine the frequency of the third harmonic for a closed-open pipe, we can use the formula:
f = (2n-1) * (v/4L)
Where:
f = frequency of the harmonic
n = harmonic number (in this case, 3 for the third harmonic)
v = speed of sound in air
L = length of the pipe
First, we need to determine the speed of sound in air at 21.5 degrees Celsius.
The speed of sound can be calculated using the formula:
v = 331.5 + 0.6 * t
Where:
v = speed of sound in meters per second (m/s)
t = temperature in degrees Celsius
Let's substitute the temperature (t = 21.5 degrees Celsius) into the formula to find the speed of sound in air:
v = 331.5 + 0.6 * 21.5
v = 331.5 + 12.9
v = 344.4 m/s
Now we know the speed of sound is 344.4 m/s.
Next, we need to convert the length of the pipe from centimeters to meters:
L = 57.5 cm = 0.575 meters
Finally, we can calculate the frequency of the third harmonic using the formula:
f = (2n-1) * (v/4L)
f = (2 * 3 - 1) * (344.4 / (4 * 0.575))
f = (6 - 1) * (344.4 / 2.3)
f = 5 * 149.74
f = 748.7 Hz
Therefore, the approximate frequency of the third harmonic for the pipe is 748.7 Hz, rounded to three significant figures.