Introductory Laboratory Category

2002 AAPT Apparatus Competition,    Boise State University

 

Name:  Robert Bishop

 

Address:        Physics Department

                        The Colorado College

                        14 East Cache la Poudre Street

                        Colorado Springs, CO  80903

                       

Phone:           719-389-6582

Fax:                719-389-6322

E-mail:            lbishop@coloradocollege.edu

 

 

 

Apparatus Title:  Sound Construction: A Doppler Effect Experiment

 

Abstract (40-50 words)

 

For introductory physics, the Doppler effect has been an elusive and difficult subject to measure quantitatively and is usually reserved for advanced laboratories with expensive equipment and complicated setup and procedures.  Qualitatively, the effect is often related by example or demonstration:  changing pitch of a locomotive horn or circular swinging of a buzzer.  Described herein is an experimental setup using ultrasonic transducers interfaced with a computer and software which is easy to construct, yields acceptable data and allows an accessible ‘view’ of the Doppler shift.

 

 

Equipment required to construct apparatus:

 

Quantity           Description                                                     Source                                     Cost

 

1                      Control, dimmer, Leviton, 600w                     Home Depot                            $03.95

1                      Motor, fan, 120 Vac                                        WalMart                                    39.95

1                      plexiglas, scrap pieces                                                on hand                                      00.00

1 ft                   pipe, PVC, ½ in ID                                                      “                                    00.00

35                    screws, bolts                                                               “                                    00.00

1                      bolt, hex head, ¾ inx2 in                                 True Value                                01.00

4                      40kHz Transducers, paired                             Marlin P Jones & Assoc.          21.96

4                      32.8kHz Transducers, paired                                      “                                    21.96

4                      25kHz Transducers, paired                                         “                                    21.96

10                    40kHz crystals                                                 Digi-Key                                   03.50

10                    32.8kHz crystals                                                          “                                    10.25

10                    26.667kHz crystals                                                      “                                    10.25

6                      pc boards, 276-159                                         Radio Shack                              10.14

10 ft                 hook-up wire                                                   on-hand                                     00.00

50 ft                 speaker wire, 24 ga, 278-1301                       Radio Shack                              03.19

20                    DB f connector pins                                        on-hand                                     00.00

2                      terminal connector, 274-679                           Radio Shack                              02.59

10                    hex inverters(MC14049), 511-4049U             Mouser Electronics                   03.80

3                      16 pin DIP sockets                                          on-hand                                     00.00

3 ft                   solder                                                                          “                                    00.00

20                    O-rings                                                                        “                                    00.00

                                                                                                Total                                        154.20

 

 

Equipment required to utilize apparatus:

 

1          MPLI with software, Vernier Software, www.vernier.com, $310.00

1          computer, PC  133 Pentium, discarded                                      00.00

1          calculator, scientific                                                                   15.00 & up

 

After using a related example: a railroad locomotive horn or whistle sounding; or a simple demonstration: the circular swinging of a buzzer, both employing pitch, the acoustic Doppler effect may be qualitatively evaluated in class.  For the laboratory, a number of quantitative procedures have been created1-6 for the evaluation of the Doppler shift with varying degrees of difficulty, mostly difficult.

The experimental setup presented herein is relatively easy to construct and yields acceptable data.  The physical setup is composed of a rotating arm with an ultrasonic transducer-transmitter source (the moving source) mounted at a user prescribed distance from the center of rotation and a stationary ultrasonic transducer-receiver (the stationary observer) oriented at a tangent to the rotational transmitter at a non-obstructive distance from the rotating arm.

The circumstance chosen for evaluation is that of a sonic source in motion and an observer/detector at rest, which lends a ‘view’ somewhat analogous to that of the Doppler shift for light.  The terms approaching and receding will be in reference to the motion of the moving transmitter to that of the stationary receiver.

Two relations,7

                        Approaching                                        Receding                  

 

                        fobs = (1/(1-vs/v))*fs                            fobs = (1/(1+vs/v)*fs

where

            fobs = detected frequency(receiver)

            fs    = stationary source frequency(transmitter)

            vs   = velocity of source(m/sec)

            v    = velocity of sound

 

are solved for vs (with A & R  =  Approaching and Receding )

 

                        vAs  =  v(1-(fs/fobs))                             fRs  =  v((fs/fobs)-1)

 

Both of these values for the velocity of the source(transmitter) as respective values for the approaching and receding frequencies may be compared to the observed and calculated velocity of the moving transmitter as noted in Figure 1.

 

The apparatus(with construction notes and see equipment/parts list):

 

(1)  Rotating arm: wood or Plexiglas, 110 cm long, 5 cm wide, 2 cm side-wall, mounted on/to a vertical shaft(shaft may need an extension) of a motor(typical box circulating fan motor) encased with wood or Plexiglas and controlled by a dimmer/motor control switch with Velcro attached to upper surface of arm to attach the transmitter and circuit.

(2)  Transmitter(s):  Ultrasonic transducer(transmitter type) electronically linked to a powered oscillator circuit(powered by a 9 volt battery) illustrated in figure 2.

(3)  Receiver(s):  Ultrasonic transducer(receiver type), the output of which is amplified by a single transistor amplifier circuit or operational amplifier, Figure 3, and the output of this is connected to the voltage input of channel A of the MPLI(described below).

(4)  Detector: Vernier Software MPLI(multipurpose lab interface) with ISA bus card and MPLI software and a computer(PC-Pentium class), optional printer.

(5)  Photogate timer: standard photogate and timer unit or a constructed photogate timer: used to time period of rotation of the arm.

(6)  Meter stick or equivalent: used to measure center of transmitter to center of rotating arm.

 

Procedure(with notes):

(1)  Mount transmitter on rotating arm(Velcro) approaching or receding relative to detector(receiver).

(2)  Place receiver(detector) in line of sight of transmitter(an optional oscilloscope/display will facilitate observance of optimal[high amplitude] waveform and is interesting to observe; 5 MHz type will do).

(3)  Adjust rotation to the desired velocity: using photogate timer to determine velocity.

(4)  Use MPLI software which displays three items: voltage versus time; FFT analysis of voltage versus time; and tabulation of data and FFT calculated values.

The voltage versus time display will indicate whether data from the detector(receiver) is indicative of the best position of the line of sight orientation of the stationary or moving transmitter to the receiver(several trials will usually be necessary to ‘hit’ the right spot, but the computer is rapid in its operation- a stationary trial will indicate the desired results).  The software automatically computes the FFT of the frequencies involved and generates the peak values which are substituted(by the student) in the given equations for the comparison of the velocity values of the moving transmitter.  Multiple transmitters on the same circuit may be used( a somewhat poorer signal results- a modified circuit for more power is possible- the multiple waveform is easily analyzed by the FFT routine, however the time frame is very short and considerable manipulation of the transmitter and receiver positions with respect to the rotation speed is necessary and speeds of rotation may exceed the holding power of the Velcro retainers—SAFETY FIRST.

 

 

            Results:

                   Three different frequencies were used and these frequencies are inherent to the transducers: 26.667kHz, 32.768kHz, and 40.000kHz.  The higher the frequency, the larger the shift compared to the lower frequency transducers-this may be calculated on a what-if basis.  The velocity calculations are usually very close, 1%-5%, WITH practice in operating the setup.  Casual use of the equipment gives values at 10% -20% agreement.  The students that have seen the setup being built have, no exceptions yet, never seen a quantitative Doppler effect experiment and are reasonably impressed.

 

Other notes:  Line voltage may affect the consistency of rotation.

                     

          “The velocity of sound in air at a temperature t(oC), vt, is expressed as vt = vo(1+3.66*10-3*t)1/2 where vo denotes the velocity of sound at t =0oC”3 or vo=331 m/sec  .7

 

References

 

(1)  T. J. Bensky and S. E. Frey, “Computer sound card assisted measurements of the acoustic Doppler effect for accelerated and unaccelerated sound sources,” Am. J. Phys. 69, 1231-1236(2001).

(2)  Ray Wisman, Michael Riley, and Kyle Forinash, “Experimental data frequency measurement with a PC,” Am. J. Phys. 60, 570-571(1992).

(3)  An Zhong, “An acoustic Doppler shift experiment with the signal-receiving relay,” Am. J. Phys. 57, 49-50(1989).

(4)  D. Schiel, J. Slaets, and S. Mascarenhas, “Measurement of acoustical second-order Doppler effect as an introductory experiment to special relativity,” Am. J. Phys. 46, 211-213(1978).

(5)  R. C. Nerbun, Jr. And R. A. Leskovec, “Quantitative measurement of the Doppler shift at an ultrasonic frequency,” Am. J. Phys. 44, 879-881(1976).

(6)  George Barnes, “A Doppler experiment,” Am. J. Phys. 42, 905-909(1974).

(7)  R. A. Serway, R. J. Beichner, and J. W. Jewett, Jr., Physics for Scientists and Engineers with Modern Physics(Saunders College Publishing, Philadelphia, PA, 2000), 5th ed., pp. 530-533.

(8)  P. Horowitz and W. Hill, The Art of Electronics(Cambridge University Press, 32 East 57th Street, New York, NY, 1989), 2nd ed., p. 302.