Resonance in Closed air columns

[Fibonacci]

is is based on the experiment where we had to find the point in which tuning fork forces air inside open-ended air column into resonance, the length of the tube is altered by changing the water level in the tube.

the water level can be altered by raising or lowering a reservoir of water, thus decreasing or increasing length of the vibrational system. the first harmonic is produced when the length of the tube is smaller than the length of the tube in the third harmonic. this idea is correct, right??

ok well if this is corrrect, do you agree that the thrid harmonic will have triple the frequency of the first harmonic??

if my above assumptions are correct, then how come in my textbook it said that: increase length of the vibrational system increases the wavelength and decreases tje natural frequency of that system, conversely, a decrease in length of the vibrational system will increase the natural frequency as wavelength is decreased.
i understand this explanation from the book, but somehow it seens to condradict what i said about if the length of the vibrational system is increased, third harmonic (higher frequency)
is heard and if i decrease it the first harmonic (lower frequency) is heard.

could someone spot my mistakes or why this is so??
hoped that make sense

 

[jbsteele]

...The explanation in your textbook is correct. Increasing the length of the vibrational system increases the wavelength and decreases the natural frequency of the system. Conversely, decreasing the length of the vibrational system increases the natural frequency as the wavelength is decreased. Your experiment is examining the effect of changing the length of the tube on the resonant frequencies heard. As you increase the length of the tube, longer wavelengths will be able to resonate in the tube, producing higher frequencies. As you decrease the length of the tube, shorter wavelengths will be able to resonate in the tube, producing lower frequencies. Therefore, when you increase the length of the tube, the third harmonic (higher frequency) will be heard and when you decrease the length of the tube, the first harmonic (lower frequency) will be heard.

 

[nlightner]

I can provide some clarification on the concept of resonance in closed air columns. Firstly, it is important to understand that resonance occurs when an external force is applied to a system at its natural frequency. In the case of a closed air column, the tuning fork provides the external force and the air column has a natural frequency at which it vibrates. This natural frequency is dependent on the length of the air column.

In the experiment described, changing the water level in the tube alters the length of the air column, and thus changes the natural frequency of the system. This is because the length of the air column determines the wavelength of the sound waves produced. As the length of the air column increases, the wavelength also increases, resulting in a lower natural frequency.

Now, let's address the question about the relationship between the first and third harmonics. The first harmonic occurs when the length of the air column is equal to one quarter of the wavelength, and the third harmonic occurs when the length of the air column is equal to three quarters of the wavelength. This means that the third harmonic has three times the frequency of the first harmonic, as you correctly stated.

However, the statement from your textbook about increasing the length of the vibrational system increasing the wavelength and decreasing the natural frequency is also correct. This is because the length of the air column is directly proportional to the wavelength, and inversely proportional to the frequency. So, when the length is increased, the wavelength also increases, resulting in a lower frequency.

To address the confusion about the first and third harmonics, it is important to note that the length of the air column is not the only factor that affects the natural frequency. Other factors, such as the speed of sound in air and the material of the air column, also play a role. So, while increasing the length of the air column will result in a lower natural frequency, it may not necessarily correspond to the third harmonic.

In conclusion, your understanding of the concept is correct, but it is important to consider all factors that affect the natural frequency in order to fully understand the relationship between the first and third harmonics. I hope this helps to clarify any confusion. Keep up the good work in your experiments and keep asking questions to deepen your understanding!