Decibels and the Aluminum Rod

Ring out the old

Introduction

A sound level meter can be used to investigate the intensity of the sound coming from an aluminum rod. The sound is loudest near the ends of the rod and gets quieter as distance increases. The sound intensity coming from an aluminum rod at a fixed distance decays in time.

Material

A sound level meter (for example from Radio Shack)
A solid aluminum rod 1 cm in diameter or more and 1.2 to 1.6 meters long.
A hammer
A stopwatch
A meter stick

To Do and Notice

Qualitative analysis

Hold the aluminum rod at its center.
Strike the end of the rod with a hammer.
Once the extraneous tones have decayed away and only one tone remains,
move a sound level meter toward and away from one end of the rod.
Notice that the sound level is greatest near the ends of the rod and that the sound level decreases with distance.

Hold the sound level meter at a constant distance from the end of the ringing rod.
Notice how the sound level decreases with time.

Quantitative analysis

Measure the sound level at a distance of 10 cm from the end of the rod.
The quickly move the meter to a distance of 20 cm. Note the change in the sound level. Theory predicts that the sound intensity will decrease proportional to the inverse square of distance. So doubling the distance should decrease the sound intensity by a factor of 4. This would be measured as a decrease in the sound level of 6 dB. Try other distances, 1 meter,2 m, 4m, 8m etc. Plot loudness versus distance.

Measure the sound level as a function of time. Keep the meter at a constant distance from the end of the rod. Time how long it takes the sound level to drop from 80 dB to 70 dB then from 70 dB to 60 dB. If the decay is exponential as predicted the times should be the same. You could also time how long it takes for the sound level to drop by 3 dB. This corresponds to the half-life of the sound energy in the rod, since a 3 dB drop in sound level corresponds to a halving of intensity.

What’s Going On?

Ears hear the pitch of a sound which corresponds to the frequency of the sound.
Ears hear loudness which corresponds to the intensity of a sound.
Intensity is measured in watts per meter squared. Intensity measures the amount of energy crossing an area per second.
Meters are designed to measure something like what the human ear hears as loudness, what is measured by the meter is called the sound level, L.
It is measured in decibels, dB.

In this experiment.
The sound level meter measures the decibel level of the sound produced by the rod.
The sound has an intensity, I, in Watts per square meter.
The sound level, L, in decibels, dB, is the base 10 logarithm of the ratio of the intensity of the sound to a reference intensity,times 10.
The reference intensity, I
0, is the quietest intensity that a human can hear and is
I
0 = 10-12 Watts/m2
so
L = 10 log (I/I
0)

So a sound intensity of 10-5 Watts/m2 has a sound level of 70 dB.
A sound that is ten times as intense has a sound level of 80 dB.
So adding 10 to the sound level multiplies the intensity by 10.
Doubling a sound intensity adds 3 to its sound level.
A 73 dB sound is twice the sound level as a 70 dB sound.

The longitudinal sound wave in the rod moves most air at the ends of the rod and so is loudest at the ends of the rod.

The intensity of the sound depends on the amplitude of the motion of the ends of the rod. The greater the motion the more intense the sound. In addition, the greater the motion the faster the energy leaves the rod as sound. So loud sounds carry away more energy than quiet ones. The result is that when the rod has more energy it loses energy more quickly and the decay has a half-life. It is exponential. It takes the same amount of time to decrease to half of its initial value.

Etc

The decibel meter is modeled on the human ear which perceives sound loudness on a logarithmic scale. To understand human perception you need to understand logarithms.

 Scientific Explorations with Paul Doherty © 2001 21 Feb 2001