Frequency & Length of Resonating Pipes

[mgiddy911]

I have completed a lab on sound waves in which we measured the speed of sound in air(a vaccum) by measuring the lengths of pipes that would resonate tunning forks fundamental frequencies. One question I am asked to answer is to describe the relationship between the frequency of a sound and the length of a pipe that resonates it and explain why the relationship is what is it. By looking at my datd I can't see a relation between the two...
(384Hz, 19.8cm) (426.7Hz, 19.9cm) (480Hz, 18.7cm) those were closed pipes and then (256Hz, 71.8cm) and (288Hz, 58.4cm) those were open pipes. From that data I don't see a relation between the frequency and the length that resonates it, am I missing somehting or did I just come up with bad data, mind you when I calculated the speed of sound I came up with an average of 341 m/s so It was farily close to the accepted value.

 

[Andrew Mason]

(384Hz, 19.8cm) (426.7Hz, 19.9cm) (480Hz, 18.7cm) those were closed pipes and then (256Hz, 71.8cm) and (288Hz, 58.4cm) those were open pipes. From that data I don't see a relation between the frequency and the length that resonates it, am I missing somehting or did I just come up with bad data, mind you when I calculated the speed of sound I came up with an average of 341 m/s so It was farily close to the accepted value.

It looks to me like your open pipes correspond to 1/2 wavelengths. Your closed pipes are approximately 1/4 wavelengths. The data seems to be a little off though.

AM

 

[wais]

The relationship between the frequency of a sound and the length of a pipe that resonates it is a direct relationship. This means that as the frequency of the sound increases, the length of the pipe that resonates it also increases. This is known as the inverse proportionality law.

In your data, it may seem like there is no relationship between the two because the changes in frequency and length are not consistent. However, if you plot the data on a graph, you will see that there is a general trend where as the frequency increases, the length also increases.

The reason for this relationship is due to the fact that the length of the pipe determines the wavelength of the sound wave that can resonate within it. The fundamental frequency of a sound wave is directly proportional to its wavelength. Therefore, as the frequency increases, the wavelength decreases. In order for a pipe to resonate a specific frequency, its length must be proportionate to the wavelength of that frequency.

In your lab, it is possible that there were some errors in measurement or experimental conditions that may have affected the data. However, your calculated speed of sound being close to the accepted value suggests that your data is fairly accurate.

In conclusion, there is a direct relationship between the frequency of a sound and the length of a pipe that resonates it. This is due to the inverse proportionality between frequency and wavelength. Your data may not show a clear relationship, but it is likely that there is a general trend that can be observed when plotted on a graph.