Question

i needed to ask 2 questions real fast please cuz i dont get how to solve:
1-An open tube 34 cm long resonates in its second overtone with a tuning fork. The air temperature in the room is 15 degrees. Calculate the wavelength of the sound waves and the frequency of the tuning fork.
2-An open organ pipe has a fundamental frequency of 212 Hz at room temperature 20 degrees. What is the length of the pipe?
Please explain what i have to do for both. I am really confused. Thanks

Answer 1

Answer on question #64440, Physics / Other

Question 1-An open tube 34 cm long resonates in its second overtone with a tuning fork. The air temperature in the room is 15 degrees. Calculate the wavelength of the sound waves and the frequency of the tuning fork. 2-An open organ pipe has a fundamental frequency of 212 Hz at room temperature 20 degrees. What is the length of the pipe?

Solution 1. The fundamental frequency is connected to length of tube as

$f_{0}=\frac{c}{4L}$

where $c$ is speed of sound. Here we suppose that tube is one-end-opened. The speed of sound is

$c=(331.3+0.606\cdot\vartheta)$

where $\vartheta$ is the temperature in degrees Celsius. Hence

$c=331.1+0.606\cdot 15=340.19\,m/s$

Hence, fundamental frequqency is

$f=\frac{340.19}{0.34\cdot 4}\approx 250\,Hz$

Then, second overtone is

$250\cdot 4=1000\,Hz$

The correspondent wave lenght is

$\lambda=\frac{c}{\nu}=\frac{340}{1000}=0.34\,m$

2. Again lets first find speed of sound

$c=331.1+0.606\cdot 20=343.2\,m/s$

Then length is

$L=\frac{c}{4f_{0}}=\frac{343.2}{4\cdot 212}\approx 0.40\,m$