Singing Rods

Introduction

Most waves need a medium to propagate through—such as water or air. In this demonstration, “singing rods” will be used to investigate waves that resonate in solid metal, and the origin of the Doppler effect will also be demonstrated.

Concepts

• Resonance
• Harmonics
• Doppler effect

Materials

Safety Precautions

Please review current Safety Data Sheets for additional safety, handling and disposal information. Be sensitive to anyone who might have a hearing problem. Use care when handling the rosin. This fine powder can easily cause a mess. Wash hands with soap and water when this demonstration is complete. Wear safety glasses. Follow all normal laboratory safety guidelines.

Disposal

The materials may be saved and stored for future demonstrations.

Prelab Preparation

Pour a small amount (≈ 5 grams) of rosin into a weighing dish, watch glass or small beaker. Only a small amount of rosin on the fingertips is necessary. Use as little rosin as possible to prevent a large mess.

Procedure

Part I. Singing Rods 

1. Obtain the three aluminum rods, aluminum tube and a small amount of rosin.
2. Begin with the long, thick aluminum rod.
3. Pinch a small amount of rosin between your thumb and index finger.
4. Hold the aluminum rod vertical and at its mid-point.
5. Lightly bang the end of the aluminum rod on the tabletop to initiate a small vibration. There should be a soft humming or buzzing sound.
6. As the rod hums, pinch the middle of the rod between your rosined finger and thumb and slide your fingers down the rod. Adjust the pinch “firmness” accordingly to allow your hand to slide smoothly down the rod.
7. Repeat step 6 three or four times until the rod begins to hum loudly. Again, be sure to pinch firmly as you slide your fingers down the rod and hold the rod at its midpoint with your other hand (see Figure 1). Caution: Do not allow the aluminum rod to “sing” so loudly that it hurts your ears or disrupts other classrooms.
   {13541_Procedure_Figure_1}
8. When the “singing rod” stops humming or gets too quiet, repeat steps 3–7 as often as necessary until students have completed their observations.
9. As the aluminum rod “sings,” if possible, show the students the motion at the ends of the rod. Students should record their observations in the worksheet.
10. Hold the aluminum rod at different locations and repeat steps 3–7 to produce resonance, if possible. Are there any other holding locations that will allow the aluminum rod to resonate? Students should record their observations in the worksheet.
11. Repeat steps 1–10 using the three remaining “singing rods.” Students should listen to the tones of each “singing rod” and note any similarities or differences. Are there different locations where these “singing rods” can be held and still be made to resonate? Students should record all their observations in the worksheet.

Part II. Doppler Effect

1. Obtain the thick, 24" aluminum rod and a small amount of rosin.
2. Repeat steps 3–7 (Part I) with the thick, long aluminum rod to produce resonance.
3. As the rod “sings,” hold it vertically and rotate (twirl) the top end away from the students and then toward them several times. Does the sound change? How? Students should record their observations in the worksheet.
4. Rotate the singing rod faster. How does the sound change now? Students should record their observations in the worksheet. The materials may be saved and stored for future demonstrations.

Student Worksheet PDF

13541_Student1.pdf

Teacher Tips

• This kit contains enough materials to perform the demonstration almost indefinitely. Use only a small amount of rosin for each demonstration. Prepare copies of the Discussion for each student, if desired.
• This demonstration can reasonably be completed in 20 minutes.
• The rosin may come in the form of a bag or in a bottle. If the rosin comes in a bag (a baseball pouch), remove the paper from the cloth bag and then place the cloth bag full of rosin back into a zipper-lock bag. The porous cloth bag can create a mess if not kept inside a secondary container.
• Whether the rosin comes in a bag or a bottle, we recommend placing a small amount of rosin on a watch glass or weighing dish for use during the demonstration.
• Clean up rosin spills with a paper towel.
• Disposable latex gloves can also be worn in place of coating fingers in rosin. The friction from the gloves will also cause the rods to “sing.”
• Of the various chemicals tested, natural pine rosin was found to be the best resonating material for the “singing rods.” Other chemicals including talc, magnesium carbonate, and calcium carbonate (chalk), powder showed very limited success.
• Use computer- or calculator-based technology equipment or an oscilloscope with a microphone to observe and measure the sound frequencies produced by the resonating singing rods. Compare the wave patterns to those predicted.

Sample Data

Part I. Singing Rods

Aluminum rod, thick, 24"

The ends of the humming aluminum rod vibrated very quickly initially, but then the motion appeared to stop while the humming continued. When the ends were touched, the sound stopped. When the humming was louder, the initial vibrations were larger, but the vibrations always appeared to stop even when the aluminum rod continued to “sing.”

There was difficulty getting the aluminum rod to resonate at other points along its length. When held at about one-quarter length, the aluminum rod resonated with a higher-pitched sound. (The aluminum rod will also resonate when held at the ⅙ length.)

Aluminum rod, thin 24"

This rod also began to hum with a very similar pitch to that of the thicker rod. The sound did not last as long as it had with the thicker rod. It too resonated when held at one-quarter of its length, and it hummed with a higher pitch at this holding position.

Aluminum tube, 24"

The tube again hummed with a similar pitch to the thick and thin rod. The “singing” appeared to be louder, but had the same pitch. It did not appear to matter that it was a tube instead of a solid rod.

Aluminum rod, thick, 18"

The shorter aluminum rod produced a higher-pitched sound than the longer rods or tube. It was harder to resonate the shorter rod compared to the longer ones. A very high-pitched sound was heard when the short rod was held at the one-quarter position.

Part II. Doppler Effect

When the “singing rod” end moves away (from the students), the sound produced by the singing rod appears to drop to a lower pitch. When it moves closer (to the students), the pitch appears to increase. Rotating the “singing rod” quickly resulted in lower and higher pitches.

Answers to Questions

1. Why do the aluminum rods resonate and “sing” when they are rubbed with the rosin? What is the purpose of the rosin?

   The aluminum rod resonates because the rod is relatively uniform and the material has a natural vibration frequency. Rubbing the rod with the rosin helps generate vibrations which tend to vibrate in one of the natural resonance frequencies of the metal rod. Holding the rod in the middle allows one fundamental harmonic frequency to resonate predominantly. Holding the rod at one-quarter of its length also produced resonance. Holding it at the end did not produce any resonance (or vibration of any kind). The rosin increases the friction between the fingers and the rod, which helps to increase the vibrations in the rod as the fingers stroke it.

2. At what point on the aluminum rod does the sound appear to be produced?

   The sound appears to be “emitted” from the ends of the rod.

3. Why must the aluminum rod be held in the middle in order for resonance to occur? Are there any other positions where the aluminum rod can be held that will produce resonance?

   The middle of the aluminum rod represents a node for the resonating frequencies of the metal rod. A node is a place where no vibration occurs in a standing wave. So, holding at a node will not affect the vibrations. Holding the aluminum rod at an antinode (maximum amplitude) position will prevent the rod from resonating. Other nodes occur at the one-quarter position for the 3rd harmonic and at the one-sixth position for the 5th harmonic.

4. Compare the sounds produced by the four “singing rods.”

   The sounds produced by the two longer rods and the tube of the same length were all very similar in pitch. The thin rod did not resonate very long, and the tube appeared to produce a louder sound. The shorter rod produced a higher pitch than the other three longer “singing rods.”

5. Define the Doppler effect.

   See Discussion information.

6. Explain why the sound of the “singing rod” changes when the rod is rotated forward and back.

   As the vibrating rod moves forward, toward an individual, the sound wave “point sources” move with the rod and the sound waves get “bunched together.” This makes the sound appear to have a higher frequency than the original stationary sound. When the rod moves away, the “point sources” are spread further apart and the sound waves are spaced further apart than the original wave, and so the sound appears to have a lower frequency. The faster the rod is rotated, the larger the apparent change in frequency between the higher and lower range.

Discussion

All sounds originate from a vibrating object. A vibration is simply a rapid wiggling of an object. The rapid back-and-forth motion of a tuning fork is a familiar example of a vibration. When an object vibrates it causes the air molecules surrounding the object to move. The rapidly vibrating object compresses the air molecules together briefly, and when the object moves away from the air molecules, a less pressurized, low-density air pocket is created. This region of lower density and pressure is referred to as rarefaction.

The aluminum rod vibrates when it is tapped by an external source. If the aluminum rod is held at a node for a specific harmonic frequency, standing waves can be produced if the vibrations continue. Stroking the aluminum rod with rosin creates vibrations in the rod due to the “stick-slip” nature of the rosin. These vibrations build on each other to create standing waves that resonate the rod at a particular harmonic wavelength. If the rod is of the proper length, this vibrating wave will produce a sound wave that can be heard. Standing waves have nodes (regions of no displacement) and antinodes (regions of greatest displacement). The wave pattern that develops in an aluminum rod is known as a longitudinal wave—similar to the waves that develop in air. For longitudinal waves, compression and rarefaction are produced. These motions are so small in the aluminum rod that they may not even be noticed. Transverse waves can also be seen initially in the “singing rod” as the ends vibrate back and forth. However, it is the longitudinal waves that resonate in the metal rod and generate the sound that is heard. This explains why the “singing rod” resonates louder the more times it is stroked. If transverse waves were supposed to resonate, the rubbing action down the length of the aluminum rod would dampen out these types of vibrations. Instead, the aluminum rod gets louder and louder, indicating that longitudinal standing waves are being produced.

The aluminum rod will resonate when it is held in the middle, at one-quarter length, and also at one-sixth length. These positions represents the first, third and fifth harmonics of the rod, respectively (see Figure 2). It would seem logical that the second and fourth harmonics should also resonate, but the rigidness of the rod limits the mid-point of the metal bar from acting as an antinode. The “singing rod” works best when the midpoint is a node.

The Doppler effect occurs when there is a frequency shift due to the relative motion between the source of a wave pattern and an observer. If a sound source of known frequency travels in a straight line toward one individual and away from a second individual, both individuals will hear a sound of a different frequency than the “known” source frequency (see Figure 3). The individual in front of the moving source will receive the sound waves more frequently than they are actually produced by the sound source. Therefore, the sound that this individual hears will have a higher pitch than what is actually being emitted by the sound source. The individual observing the sound source as it moves away will receive the sound waves less frequently than they are actually produced by the source. This observer will hear a lower pitch compared to the actual pitch of the sound source. An observer traveling at the same speed and direction as the sound source will hear the true frequency of the sound because there will be no relative motion between the source and the observer. As the “singing rod” rotates toward an individual, the pitch will increase. As the end of the “singing rod” moves away, the pitch will decrease.