🚀 go-pugleaf

            TWO TUNING FORK ACTIVITIES ARE DESCRIBED BELOW
You need a laser, a decibel meter and a tuning fork mounted on a resonant
box. Clamp the tuning fork box to a table and place a common decibel meter
in front of the box opening. Hit the fork and see the decibel level decreasing
from about 110 to 80 decibels in twenty seconds or so. Good data can be
collected in several soundings of that duration. A large church bell, if it
were available, would be a much better source of sound for this activity. But
we must learn to use what we have.

1. Ask a group of students to record decibels and the time of recording in
   front of the class. Write the results on the blackboard. Then ask the class
   to convert decibels into sound intensities, using the formula which defines
   decibels. The data my students collected are shown in the first two rows
   below;. The last two rows show sound intensities I, (in milliwatts per
   square meter), and common logarithms of I. Do not tell students that the
   curve is exponential; they should be able to recognize this (with a hint
   from you) by discovering that the plot of (log I) versus time t is linear.
   The data below show that the "half-life of sound" was about 2.3 seconds.
   (A radioactive source of a convenient half-life, and a Geiger counter, can
   also be used to collect good data on the law of exponential dependence.)

    S (dB)       105     100        95       90       85      80       75
    t(sec)       0.0     3.2       7.0     11.1     15.5     ...       ...
    I (mW/m*m)  31.6     10.0      3.16    1.00     0.32     ...       ...
    logI        1.50     1.00      0.50    0.00    -0.50     ...       ...

In practice it was more convenient to read times at predefined sound levels
than to read decibels in predetermined times. The numbers in the second row
are mean times from four measurements. Good data below 85 dB are certainly
obtainable in a quiet room. In fact, you can ask students to predict times
corresponding to 80 and 75 dB (extrapolating the curve) and verify
predictions by direct measurements.


2. How does the sound intensity depend on the amplitude of oscillation? Do
   not tell them that I is proportional to the square of A. But first show
   that for any power function (y proportional to x raised to the n'th power)
   the plot of (log y) versus (log x) is a straight line. The slope of that
   line is the value of n, provided scales are identical along the two axes.
   Now comes the experimental part. The amplitudes of the tuning fork prongs,
   typically 1 mm or less, are too small to measure directly. But measurements
   with a ruler become possible if a bit of a common mirror is fixed to the
   ending of one prong (with a strong glue). Let the laser beam be reflected
   from that mirror and observe the beam swing on a distant wall. At a
   distance of about 10 meters the swings of the beam, A, are already large
   enough to measure. The data collected by my students are shown in the
   first two lines below. Results of processing are shown in lines 3 to 5.

   S (dB)        107    105    103    100     97     95     93     90    85
   A (cm)       20.6   16.9   13.2    9.9    6.7    5.4    4.0    3.0   1.7
   I (mW/m*m)   50.1   31.6   20.0   10.0   5.01   3.16   2.00   1.00  0.32
   logI         1.70   1.50   1.30   1.00   0.70   0.50   0.30   0.00  -0.5
   logA         1.31   1.23   1.12   0.99   0.82   0.73   0.60   0.48  0.23

   The slope obtained directly from the plot of (log I) versus (log A) shows
   that n=2. The least square fit to the first 8 data points above leads to a
   conclusion that n=1.99 plus or minus 0.03. Not bad for commonly available
   equipment!  (In case you do not know, a digital sound meter, with a range
   from 60 to 120 dB, can be found in a Radio Shack store for 60 dollars. The
   catalog number of that item is 32-2055.)

  Trivial? Yes. Useful? I hope so. Ask for help if needed. And please share
  your data if you are able to perform experiments with a church bell.

           Ludwik Kowalski          kowalski@apollo.montclair.edu