Resonance

What is resonance? Does the length of the tube change its natural frequency?

SCIENTIFIC PRINCIPLE

The scientific principle of Resonance will be explained in this section.

Resonance is when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion. A resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. When the natural frequency of an object is reached the object begins to oscillate and create a standing wave pattern. For a specific there are a specific wavelength and frequency that is associated with the number of harmonics.

INTRODUCTION

Observe the different natural frequencies of tubes of different lengths

MATERIALS

Tubes of different sizes

Tuning Forks

PROCEDURE

1.Pick the tuning fork that matches the note on the tube.

2. Use the mallet to vibrate the tuning fork.

3. Hold the tuning fork near the end of the tube and listen for the sound. The natural frequency will resonate and produce a loud noise.

4. Hold the vibrating tuning fork to another tube and observe the difference when it does not make a sound or a weaker sound than that of the tube which matches the natural frequency.

It should sound like this:

1. How many different resonant frequencies can there be for an open or closed pipe (one end closed), and how is resonant frequency for mathematically related to pipe length l for both closed and open-end pipes? It can have as many different frequencies as it has different harmonics with open tubes going in increasing number and closed pipes only resonating at odd intervals. The pipe length is inversely related to resonance since the speed of sound is divided by 2 or 4 times the length (open and closed respectively) in order to find the resonating frequency and then all of its harmonics.

2. You know that a tube (open or closed) can resonate in air, but can a tube resonate under water? If no, explain why not; if yes, does it resonate at the same frequencies as it did in air? Why or why not? The tube can resonate in water because it is still a medium thorugh which sound and waves can travel. However the tube will resonate at different frequencies than it did in the air because the speed of sound in the water is much different to the one of the air.

3. If you had a tube with open ends that was 19.1 cm long, what frequency sound wave would you need to drive down the tube to have it resonate with 3 standing wave nodes inside the column?

This would be the third harmonic so you would multiply the fundamental frequency by 3 which is 3(344 m/s /(2*0.191m)which is 2701 Hz.

4. Assuming you had the ability to adjust the length of the tube from the previous question, then without changing the driving frequency, how much longer would you have to make the pipe to reach the next resonant mode? How many standing wave anti-nodes are present inside the tube at the next resonant mode? Going from a third resonance to a fourth resonance increases the number of antinodes from four to five, and because the driving frequency hasn’t changed, the wavelength of the sound wave hasn’t changed either. This means that the length must increase to be equal to ½ wavelength which will then result in a fifth in a fifth standing wave so the length of the wave would have to change since the frequency did not.

5. Opening or closing the finger holes on a recorder flute will effectively shorten or lengthen the air column on the instrument. If the highest frequency the recorder can play is 2,850 Hz and the lowest is 344 Hz, what is the distance between the first finger hole and the end of the flute?The highest frequency would be at .0603 m and the lowest frequency would be at .500 m. The distance between the first finger hole and the end of the flute is therefore .440m.