Competency

Wrap a solenoid.

Design Challenge

Design, build, and evaluate a speaker.

Resources

• Sound Level Meter

Introduction

A 3D printer was used to fabricate a linear motor in Lab 2. When an alternating current is sent to the solenoid in the linear motor, the magnet moves in one direction when the voltage is positive, and moves in the opposite direction when the voltage is negative. The linear motor, therefore, is an alternating current (AC) motor.

In subsequent labs, three different methods of alternating the current to move the magnet back and forth were employed:

1. The leads of two wires connected to the terminals of the motor were alternately switched between the positive and negative terminals of a battery.
1. A battery was rotated to alternate the direction in which the current flowed.
1. A waveform generator was used to generate an alternating current.

The first two methods can be readily followed. The sine wave produced by the waveform generator is more abstract, and requires more explanation. Many freely vibrating objects in nature produce a sine wave as they move back and forth. For example, in the figure below, a student in the Laboratory School for Advanced Manufacturing is pulling a strip of poster paper beneath a paint bucket swinging from a rope.

Paint flowing from a nozzle at the bottom of the bucket traces a pattern on the paper beneath it. The pattern that appears as the paint bucket swings back and forth is a sine wave. A moment’s thought suggests the reason that the pattern traced is a sine wave. As the bucket reaches the top of its arc, it gradually moves more and more slowly. At the top of the arc, gravity slows the bucket almost to a complete stop. At that point, the bucket reverses direction, falling back toward the center.

 Table 1. Movement of Bucket from the Center Line to the Top of the Arc Time (in seconds) 0 1 sec 2 sec 3 sec 4 sec 5 sec 6 sec Distance Traveled 0 26% 50% 70% 86% 98% 100%

The bucket, therefore, is traveling at its fastest rate as it moves through the center line, and begins to slow due to the force of gravity as it moves back toward the top of the arc. If it takes the bucket six seconds to travel from the center line to the top of the arc, it will move 26 percent of the way during the first second. It will reach 50 percent of the total distance by the end of the next second. It will reach 70 percent of the way by the end of the third second, beginning to slow down as gravity exerts its force. It will only travel another 12 percent of the distance during the fifth second, moving from 86 percent of the way to 98 percent of the total distance. During the sixth second, the bucket will only travel another 2 percent of the way, moving from 98 percent of the way to 100 percent of the total distance in the final second. At that point, the bucket begins to fall back toward the center line, picking up speed as it moves toward the midpoint.

If the distance traveled during each second of movement is plotted on a graph, the resulting pattern is a sine wave, as shown in the figure below.

In this instance, it took the paint bucket 24 seconds to make one complete back-and-forth movement. At this rate, the paint bucket would complete two and one-half cycles in one minute: one cycle in the first 24 seconds, a second cycle in the next 24 seconds, and a half-cycle in the last 12 seconds. Consequently, the bucket travels back and forth at a rate of 2.5 cycles per minute. If the rope were shortened, the bucket might travel back and forth at a rate of 3 complete cycles per minute. The number of times that a freely vibrating object moves back and forth during a given time period is known as the frequency. The term frequency refers to how frequently an object moves back and forth in a given time period.

The amount of time required to complete one cycle is known as the period. If the bucket is moving back and forth at a rate of 3 cycles per minute, the period would be one-third of a minute (i.e., 20 seconds). The period of a freely vibrating object is the inverse of the frequency. For example, if the frequency is 3 cycles per minute, the period will be 1 / 3 of a minute.

 Table 2. The period is the inverse of the frequency. Frequency Period 3 cycles per minute 1 / 3 minute

Frequency is one of two major attributes of a vibrating object. Amplitude is the second attribute. Amplitude in this instance refers to the distance that the paint bucket travels from peak to peak as it moves back and forth. If the farthest point that the paint bucket travels in each direction is one meter from the centerline, the total distance measured from peak to peak would be two meters. In that case, the movement of the bucket could be said to have an amplitude of two meters.

It is possible to visually follow the movement of an object up to a frequency of approximately 15 or 20 times per second. After that, the eye cannot track the movement. This phenomenon causes film (projected at a rate of 24 frames per second) and video (projected at a rate of 30 frames per second) to be perceived as one continuous movement. Once the rate of movement exceeds a frequency of 60 times per second, it is perceived as sound. Movement that falls between a frequency of 20 and 60 times per second is not perceived either visually or auditorily. However, it may be possible to perceive the movement as a tactile vibration at that frequency. The term Hertz (abbreviated “Hz”) is now used to refer to cycles per second, in honor of the scientist, Heinrich Hertz.

The concepts of frequency and amplitude introduced through the context of the paint bucket pendulum apply to mechanical, acoustic, electrical, and electromagnetic systems. Therefore, it is worth taking the time to understand the underlying phenomenon since it will be useful across a variety of disciplines that include sound and music, mechanical systems such as the linkages coupled to the linear motor in previous labs, electronics, and mathematics, among others. For example, the term “sin (x)” in trigonometry is just a way of describing the distance that the object travels at a given phase in the cycle. Much of mathematics was originally developed to describe natural phenomena such as this. Today, these concepts are often taught out of context, making them abstract and difficult to understand.

Wrapping a Solenoid

In the series of FabNet Invention Kits developed in collaboration with the Smithsonian Institution, the Linear Motor Invention Kit was developed to provide scaffolding for the Telephone Invention Kit. As you have seen in Lab 3, a speaker is simply a linear motor with cone that amplifies the sound. As the frequency of the waveform generator is increased to 60 cycles per second or above, a clearly discernable tone can be heard. It just is not very loud. Adding a speaker cone focuses and amplifies the sound.

The solenoid used to construct the linear motor was provided with insulated magnet wire already wrapped around the solenoid tube. In this lab, you will have an opportunity to wrap the magnet wire around the solenoid tube yourself. A battery-operated winder is used to accomplish this task.

Directions for using the winder to wrap magnet wire around the solenoid tube are found on the Make to Learn web site here:  https://maketolearn.org/inventions-kits/solenoid/make-2/

The process of wrapping the magnet wire around the solenoid tube typically takes about five minutes. The process is straightforward. Mastering this skill has two benefits. Completing every step of fabricating and assembling a solenoid removes the mystery from the process. It also allows you to design solenoids for specific purposes and uses. Ampere discovered that the strength of a magnetic field generated by a solenoid depended on three factors:  (1) the diameter or gauge of the wire, (2) the number of wraps or turns around the solenoid tube, and (3) the length of the solenoid tube.

Increasing the number of wraps increases the strength of the magnetic field produced. The insulation on magnet wire is a special varnish that is a very thin coating. This allows more wraps of wire to be wound in a given space, increasing the strength of the magnetic field. To create a more powerful linear motor, therefore, more wraps of wire could be added to the solenoid tube.

In the case of the linear motor, the solenoid tube is placed on supports, allowing the magnet to move freely back and forth. The construction of most dynamic speakers is slightly different. The permanent magnet is usually attached to a fixed base so that it cannot move. The magnetic field generated by the flow of current through the solenoid wire, therefore, causes the coil of wire to move back and forth. The coil of wire is attached to the speaker cone or diaphragm. The movement of the coil of wire consequently causes the speaker diaphragm to vibrate, producing sound waves.

If there are too many wraps of wire in the solenoid coil, it may be so heavy that it is unable to move the weight of the coil efficiently. Consequently, the design specifications for an efficient linear motor and an efficient speaker may differ. However, in the case of the FabNet Linear Motor Invention Kit and the FabNet Speaker Kit, we chose to make a pedagogical point. We wanted to emphasize that the same solenoid can be used in both a linear motor and in a speaker. Using the same solenoid for both makes it apparent that a speaker is in actuality a linear motor with a speaker cone attached.

To accomplish this pedagogical goal, the specifications for the solenoid used in both invention kits is a compromise between the ideal design specifications for a linear motor and the ideal design specifications for a speaker. Once you understand the underlying principles, however, you can then employ the design that is best suited for a given applications.

In addition to the science and engineering concepts involved, there are also cross-disciplinary extensions to mathematics. Joe Garofalo and Kim Corum have successfully worked with middle school students in related activities in which the students derive Ampere’s Law. The mathematics concepts addressed include direct and inverse relations. Both students who have had beginning algebra and pre-algebra students were successful in this activity. In addition to the mathematics concepts learned, an understanding of Ampere’s Law is useful for understanding a range of inventions that incorporate solenoids.

Speaker Design Considerations

Objects with a greater mass vibrate more efficiently at lower frequencies. Objects with a lower mass vibrate more efficiently at higher frequencies. For that reason, speakers designed to play bass notes (called woofers) tend to be larger than speakers designed to play treble notes (called tweeters). In high fidelity speaker systems, several speakers are combined into a system that can play a range of notes with great fidelity. In some cases, the experience can closely resemble listening to a life performance.

A subwoofer can play very low frequencies that can be felt as well as heard. If the volume on the stereo amplifier is increased to a high level, a 20 Hz tone played through a subwoofer may be seen as well as heard. This provides a way of establishing that a speaker simply produces a back-and-forth movement of a diaphragm to create vibration in the air that is perceived as sound.

Even a speaker made of simple materials can sound remarkably good. For example, the speaker below (Figure 6) is made of paper, with a twist of wire wrapped around a paper tube to form a solenoid. The construction details clearly show that the magnet is attached to the base. Consequently, the wire coil moves back and forth, causing the paper cone to vibrate.

Speaker Design Challenge

The foregoing sections provides the information needed to understand how a speaker works. A dynamic speaker works in the same way as a linear motor. However, in a linear motor the magnet is usually moving back and forth at a rate of five or ten times per second. When the same solenoid is used to construct a speaker, the audible frequencies range from about 60 times per second at the low end to as many as 20,000 times per second at the high end.

1. Follow the directions on the Make to Learn site for wrapping a solenoid.
2. Follow the directions on the Make to Learn site for building the M2L Dynamic Speaker.
3. Evaluate the fidelity of the speaker.

Design Considerations. The supports that attach the solenoid to the fixed base should have some flex or springiness in them. If the supports are too rigid, the solenoid coil will not be able to move freely. If the supports are too floppy, the solenoid tube will not return to its original resting position.

Once you have designed and assembled a speaker system, attach the output of an amplifier to the leads of solenoid wire.

Then connect the audio output of a phone, tablet, or MP3 player to the input of the amplifier. Turn on the amplifier, and send some music from the MP3 player to the amplifier. Then troubleshoot any problems that you encounter, such as a loose connection, etc.

Evaluating the Fidelity of the Speaker

If a series of tones of different frequencies is played through a speaker, the speaker will not respond equally to all of the frequencies. A sound level meter is used to measure the output of a speaker.

Students in the Lab School evaluated the output of speakers that they designed, using a sound level meter to measure the output of the speaker in response to tones with frequencies of 125, 250, 500, 1000, 2000, and 4000 Hz.

The data that they collected was recorded in a table such as the one shown below.

 Table 3. Frequency response of two speakers (measured in decibels). Frequency (Hz) 125 250 500 1000 2000 4000 Speaker 1 79 dB 90 dB 57 dB 56 dB 53 dB 52 dB Speaker 2 67 dB 70 dB 72 dB 77 dB 94 dB 75 dB

The students then used a spreadsheet to graph the results, An example is shown in Figure 10 (below). Based on this figure, can you determine which speaker cone had the greater mass?

Once you have assembled and tested your speaker, evaluate its fidelity by generating a frequency response chart such as the one above. The Speaker Test Tone Generator on the Make to Learn site produces tones at intervals from 250 Hz to 8000 Hz.

Then document the process of building and testing the speaker. Record your observations about the construction process and the results of your evaluation of the speaker in a half-page report.