Monthly Archives: October 2014

Speed of sound in a test tube

Students can use free Apps on their phones to measure sound frequency and to generate tones.  Use these Apps and an ordinary test tube to demonstrate resonance and measure the speed of sound in air.  Students produce tones by blowing across the test tube and measuring frequency.  When a tone generator App producing the same pitch comes near the mouth of the test tube, it strongly amplifies the tone.  Students may relate this resonance amplification to marimba – like musical instruments.

Smart phones are expensive, but almost every student has one – everywhere in the world! Neither the school nor the teacher need to buy this powerful piece of equipment to use for physics lab.  In this experiment, students use inexpensive cell phone Apps to generate tones and to measure frequency.

  • Inexpensive cellphone Apps that work well:
    1. PitchLab, for tuning guitars, but here used for measuring frequency
    2. FG Tone Generator

    a) PitchLab (left)       b) FG tone generator (right)
  • Test tubes:  A variety of useful sizes are standard.  6″ (15 cm) tubes are easy to blow across to make a tone.  The very large ones are a little bit difficult to blow for long enough to register the frequency.  It is interesting to create tones from two tubes that differ in length by 2×, because these will produce pitches that are one octave apart — a factor of 2× in frequency.
  • Graduated cylinder:  A 100 mL cylinder can be filled to varying height with water, to show how the resonant frequency varies with air column length.
  • Open cylinders or pipes:  lengths 12″ to 18″ (~30 to 45 cm) produce resonances in a useful range.  Metal tubes and pipes are readily available at low cost.  It will be impossible to create sounds by blowing across the mouth of an open pipe.  However, it is easy to calculate the expected resonance, and then use the tone generator to excite a good resonance.  The air flow pattern and wavelength of the sound resonance may be easier to visualize in an open-end pipe than for the closed-end pipe such as a test tube (see below).
Resonant Air Flow

When the air in a test tube vibrates, the air motion must be a maximum at the mouth of the tube, and zero at the closed end.  The air motion for the fundamental (lowest possible) frequency is a ‘breathing’ mode, as indicated in the figure:  testtubeThe distance between a node (zero motion at the left end) and the next consecutive antinode (maximum motion at the right open end) is 1/4 of the wavelength.  Therefore a full wavelength is 4× the length of the test tube.

Air motion in an open tube ‘breathes’ symmetrically at both ends, so the fundamental resonance looks like: opentubeThe distance between a node and the next consecutive antinode is 1/4 of the wavelength,  so the full wavelength of the fundamental wavelength is 2× the length of the open tube.

Measuring speed of sound

I will be attaching videos here to demonstrate the open and closed tube resonances.  The procedure for the closed tube is:

  1. Measure the length, L, of the tube in meters.
  2. Blow across the end of the tube and measure the frequency, f, of the tone using PitchLab or an equivalent App.
  3. Because the wavelength, λ = L/4, the speed of sound in air is:

    c = f * λ = f * L/4

The procedure for the open tube is a little different:

  1. Measure the length, L, of the open tube in meters.
  2. Because the wavelength, λ = L/2, the fundamental frequency is: f = c/λ = 2 c/L.  Use the known value of c ≈ 340 m/s
  3. Hold the little speaker of the your cell phone very near the end of the tube.  Sweep the FG tone generator through a range of frequencies around the fundamental.
  4. When the tone gets very loud, that is the fundamental.  Read the exact value, f1.
Discussion topics
  1.  How is sound resonance used in musical instruments?
    Organ pipes, flutes, trumpets, guitars, etc., all use resonance to define the pitch of a note. The resonator can also play the part of an intermediary between the source and the room environment. Here are some pics of musical instruments that use resonators to enhance the volume of sound emanating from a vibration source. The source may be too small, or the vibration amplitude too small, to couple strongly to the air around the musical instrument.  The resonator amplifies the vibrations. Instruments
  2. Higher harmonics
    Try exciting higher harmonics in the tubes.  The second harmonic in the open tube is f2 = 2 f1.  The third harmonic is f3 = 3 f1.   For the closed tube, the second harmonic is f2 = 3 f1.  The third harmonic is f3 = 5 f1.



Lemon batteries Plus

Dissimilar metals poked into ordinary fruits and vegetables produce a measurable voltage and current.  This lab extends lemon batteries to a hands-on illustration  of circuit principles, electrochemistry, and LED semiconductors.

 The students can make lemon batteries with large enough electrodes so they have significant power capability.  They measure voltage and current outputs.  Then they connect them in various ways to produce a useful function, such as  lighting an LED.
Materials for lemon batteries that have useful power:
  • Citrus:  Usually lemons, but oranges, small grapefruits etc. seem to all work.  People have reported using potatoes, but I am not sure potatoes will provide as much current.
  • Zinc metal strips:  Galvanized steel sheet is a good source of zinc.  1/32 – inch (0.75 mm) thickness straps are a common building material for joining framing lumber together.  Try to find  straps that are about 1.25-inch wide (~3 cm).  Use a good tin-snips to cut them to  1.25″ x 5″ with a sharp corner at one end, and rounded corners at the other end.
  • Copper:   .005-inch (~0.012 mm) thick sheet was obtained from a metal-supply store.  $5- worth will be a big supply.  Snip this into 1.5″ x 5″ pieces.  Cut a point at one end.  Then bend each strip lengthwise over a table end to stiffen the material, so students can push it into a citrus fruit.    Sand or file the long edges if there are any sharp burrs along the sides.
  • LEDs.  Get different colors, including enough red ones for each group of students, as well as a couple of white LEDs.  The type doesn’t seem to be important .
 Experimental procedure and potential discoveries:
  1.  The first step is to have each small group of students assemble a lemon battery.  A typical battery is illustrated here:lemonbatteryleaf
  2.  Students then measure the voltage of the battery with a simple multimeter.  They measure the short circuit current with the multimeter in the milliampere range.
  3.  Now compare results from different groups.  If you chart the voltage and current of all the lemon batteries in your class, students can notice the following facts:
    • The voltages are all about the same, close to 1.0 Volt.
    • The currents vary widely, in the range of 0.1-0.3 mA.
  4.  Students  should be led in a discussion of why this is true, and the concepts of intrinsic and extrinsic properties will be introduced — see further discussion below.

  5.  Let each group have a red LED to attach to their battery. They must observe the polarity of the LED — the longer lead is the positive lead and must be connected to the Cu terminal, otherwise the diode cannot let current through.  However, even with the correct connection, one battery is not enough to light a red LED!
  6.  Suggest to students that they try connecting more batteries (in series or parallel?).  The reason is that LEDs have a minimum threshold voltage, and that threshold is above 1 volt.  Now you will have to darken the room, because even with two lemon batteries in series, the LED light is very dim.  However, your students will be delighted to turn their LED on and off by interrupting the circuit.
  7.  As each group gets lights their red LED, give them a white LED to try.  Actually, one of my students grabbed a white LED just out of curiosity.  The result was very mysterious:  He discovered it took three lemons in series to light a white LED, and the white LED was visible across the room without the room lights being dimmed — much brighter than the red LEDs!

When different batteries using the same materials are compared, the students find that they always see pretty much the same voltage, whereas the current differs widely between batteries. Furthermore, students connect cells to each other in different ways in order to light an LED.  Two or more are required to light a red LED;  three or more to light a white LED.  Furthermore, even though the power input is similar, the white LED is much brighter.

Discussion topics
  1.  Extrinsic and Intrinsic Properties – Battery Current and Voltage
    The voltage is an intrinsic property of the battery, depending only on the two metals.  The current depends on the area of the electrodes, their separation, and the conductivity and dimensions of the acidic material in between the two electrodes.  Current is therefore an extrinsic property — it depends on the size or amount of things.
  2.  Why was the voltage of the lemon battery about 1.0 V?
    Students who have studied chemistry will be familiar with the electromotive series, as follows:electromotiveseriesThis series shows that for any two metals, the one that is lower on the chart will ionize more readily than the metal that is higher, and therefore give up an electron to form the negative terminal of a battery made with those two metals.  The ionization energy difference translates into a voltage difference when the two metals make a battery.  The voltages in the table show that the potential difference between zinc and copper electrodes should be about .344 – (-.762) = 1.106 V.
  3.  What is the voltage of alkaline batteries, and what is the difference between AA, AAA, C and D alkaline batteries?
    Regular alkaline batteries are basically zinc and carbon batteries, and have an intrinsic voltage of 1.5 V.  The different sizes demonstrate the extrinsic property — that the charge storage of the larger batteries is greater.
  4.  What are lithium batteries used for and why?
    Lithium is even lower on the electromotive series than Potassium.  You can see that these very reactive alkali metals will make batteries with voltages above 3 V.  Higher voltage is very useful for powering some electronic devices.  Light weight also favors lithium batteries.
  5.  Why is the LED voltage threshold higher for white LEDs, and why are they brighter?
    Going from red to blue to ultraviolet LED light requires a higher voltage because the blue  photons are more energetic than red,

    LED IV curves
    Blue LEDs have a higher voltage threshold then Red

    and are produced when the electrons drop through a bigger bandgap semiconductor.  White LEDs need to have a blue component.  Notice that white LEDs are used for illumination.  That means manufacturers have optimized their efficiency.  They give a brighter light.


Student Worksheet Downloadable Word Doc

We used the following word document as a lab procedure in the PHY112 class.  However, it could be used in PHY101 as well.

PHY112Lemon Batteries

The worksheet instructs students how to make their lemon battery.  Then it tells them to measure voltage and current for their own lemon, and also tabulate and compare the results of other groups.  Finally, it asks the following questions:

  1.  What factors affect an extrinsic property of a system, and what factors affect an intrinsic property?
  2.   Why do some batteries have higher voltages than others?
  3.   What are some basic differences between an LED and an ordinary resistance?
  4.   Why is a white LED brighter than a red LED?