Measuring Your Threshold of Hearing for Sounds of Different Pitches

Objective

The objective of this experiment is to measure your threshold of hearing as a function of the frequency of the sound.

Introduction

This is an interesting experiment in the area of audio (sound) perception. The human auditory system is sensitive to a wide range of sounds, both in terms of frequency (pitch) and intensity (loudness). Typically, a young person is able to hear frequencies ranging from 20 to 20,000 Hz (Hz is the abbreviation for Hertz, the name for units of cycles/sec). Humans can also detect sounds with intensities ranging over 13 orders of magnitude (powers of ten). In other words, the loudest sound a human can perceive is 10,000,000,000,000 times as loud as the softest sound that can be perceived.

When comparing sound intensities over such a wide range, it is inconvenient to keep lugging all of those zeros around, so units of decibels (dB) are commonly used instead. A decibel is defined as 10 × log(I ⁄ I_ref ), where I and I_ref are the two intensities being compared.

So if I is 10 times louder than I_ref , that corresponds to an increase of:
10 × log(10 ⁄ 1) dB = 10 × 1 dB = 10 dB.

If I is 100 times louder than I_ref , that corresponds to an increase of:
10 × log(100 ⁄ 1) dB = 10 × 2 dB = 20 dB.

If I is 1000 times louder than I_ref , that corresponds to an increase of:
10 × log(1000 ⁄ 1) dB = 10 × 3 dB = 30 dB. And so on.

For each power of ten change in intensity, there is a decade change (±10) in terms of dB.

Our ability to detect changes in intensity (the "just noticeable difference" in loudness), is proportional to the original intensity of the sound. If you are in a very quiet room, you can hear a whisper. Another person whispering could also be heard: the added sound would be significant in relation to the existing sound level. On the other hand, if you're at a basketball game with a lot of people cheering, you're not going to be able to hear someone whispering two rows down, because now the added sound is insignificant in relation to the existing sound level. In other words, as sounds get louder, there needs to be a bigger change in intensity in order to detect it.

So you can see that decibels are used not simply for reasons of convenience, but also because when we express sound levels in decibels, we get the numbers that have significance in terms of human perception.

Decibels define a relative measure of sound intensity. In other words, it will tell you how much louder or softer one sound is than another. However, if we choose a fixed point for the reference intensity level, then we have an absolute measure of sound intensity. A reference level that is often used in human auditory science is Sound Pressure Level (SPL), the lower limit of human hearing, which is defined as 10^-12 W/m², and is given a value of 0 dB (SPL).

As we pointed out earlier, humans can hear a wide range of intensities and also, a wide range of frequencies. The lowest sound (in pitch) we can typically hear is about 20 Hz, and the highest sound 20,000 Hz. However, we are not equally sensitive at all frequencies. On average, the threshold of hearing of the human auditory system varies with frequency as shown in the following figure (ISO R226, 1961):

The curve shows the gain (amplification) required for tones at each frequency so that each tone is perceived at equal volume. Think of adjusting a volume knob for each tone, so that all of the tones sound equally loud. If the volume knobs are calibrated in dB, then reading off the volume settings for each frequency would produce this curve. From the curve, we can see that, on average, humans are most sensitive to tones at about 3500 Hz, because these tones require the least gain.

The curve shown above is an average response for a large number of human listeners. In this project, you will measure and graph your own individual threshold of hearing as a function of frequency.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

• decibels (dB)
• gain
• sound frequency (Hz)
• threshold of hearing
• auditory system
• psychoacoustics
• audio perception
• Weber-Fechner law
• Stevens' power law

Questions:

• Each of the .wav files used in the Experimental Procedure section contain a series of pure-tone sounds, each decreasing in loudness by a 3 dB step. A 3 dB decrement corresponds to what fractional decrease in loudness?
• If a sound doubles in loudness, what is the corresponding increase in units of decibels (dB)?
• Using the graph in the Introduction, how much louder does a tone at 30 Hz have to be compared to a tone at 3500 Hz in order to be perceived as equally loud? Give your answer both in dB, and as a numerical factor.
• Can you think of reasons why human hearing would be more sensitive for certain ranges of frequencies than for others?

Bibliography

• Here are two references on decibels:
  
  • http://www.sfu.ca/sonic-studio/handbook/Decibel.html
  • http://arts.ucsc.edu/EMS/Music/tech_background/TE-06/teces_06.html
• Here are two references on the human ear and auditory system:
  • http://faculty.washington.edu/chudler/bigear.html
  • http://www.neurophys.wisc.edu/h%b/auditory/anatomy/a04.html
• Here is the Wikipedia article on Psychoacoustics:
  
  • http://en.wikipedia.org/wiki/Psychoacoustics
• The following are selected references on the Weber-Fechner law and Stevens' power law, both of which describe relationships between actual physical magnitude of a stimulus and the human perception of that stimulus:
  • http://www.neuro.uu.se/fysiologi/gu/nbb/lectures/WebFech.html
  • http://en.wikipedia.org/wiki/Weber-Fechner_law
  • http://www.neuro.uu.se/fysiologi/gu/nbb/lectures/Stevens.html
  • http://en.wikipedia.org/wiki/Stevens%27_power_law

Materials and Equipment

• computer with Internet access and sound card (see Experimental Procedure section for .wav files)
• audio headphones (best quality available)
• a quiet room
• semi-log graph paper (or regular graph paper and a calculator with log function)

Experimental Procedure

You will use the following 19 .wav files for constructing your threshold of hearing vs. frequency curve. Each file contains a sequence of tones at a single frequency (pitch), but with a decrement in amplitude of 3 dB for each tone.

There are four steps which you will follow to construct your threshold of hearing vs. frequency curve. Details on each step are given below.

1. Adjust the volume on your computer for proper playback of the tones.
2. Listen to each file and count the number of tones you can hear. Repeat at least five times for each file to assure an accurate count. Allow yourself about an hour for this step.
3. Convert your count to threshold value for each frequency (see below for details).
4. Graph the results on semi-log graph paper.

Pure-Tone .wav Files
40 Hz (10 levels ~ 20 sec)	3500 Hz (25 levels ~ 10 sec)
60 Hz (15 levels ~ 27 sec)	4000 Hz (25 levels ~ 10 sec)
100 Hz (20 levels ~ 30 sec)	5000 Hz (25 levels ~ 10 sec)
200 Hz (20 levels ~ 20 sec)	6000 Hz (25 levels ~ 10 sec)
400 Hz (20 levels ~ 20 sec)	8000 Hz (25 levels ~ 10 sec)
500 Hz (20 levels ~ 20 sec)	9000 Hz (25 levels ~ 10 sec)
600 Hz (20 levels ~ 16 sec)	10000 Hz (25 levels ~ 10 sec)
1000 Hz (25 levels ~ 10 sec)	11000 Hz (25 levels ~ 10 sec)
2000 Hz (25 levels ~ 10 sec)	12000 Hz (25 levels ~ 10 sec)
	15000 Hz (20 levels ~ 8 sec)

Here are the detailed instructions:

1. Adjust the volume on your computer for proper playback of the tones.
   1. Use the best quality audio headphones available.
   2. Do your test in the quietest room available. Background noises will interfere with the sounds you are trying to hear, and may change your threshold values.
   3. Play the 3500 Hz sequence and adjust the volume so that you hear only the first 18 or 19 levels in the sequence. There are 25 levels in the file, so this means that you have adjusted the volume so that levels 20–25 are below your threshold of hearing.
   4. Write down the number of levels you can hear in the 3500 Hz sequence, and leave the volume setting unchanged for all of the other files.
2. Listen to each file and count the number of tones you can hear.
   1. Repeat at least five times for each file to assure an accurate count.
   2. Use a table to keep track of your counts (see sample table at the end of this section).
   3. Allow yourself about an hour for this step.
3. Convert your count to threshold value for each frequency.
   1. You will be plotting your results relative to your threshold for the 3500 Hz tone sequence. We will assign 3500 Hz to −4 dB, the same level as in the standard threshold curve in the Introduction.
   2. To calculate your threshold value for a given frequency, take the average count for that frequency, subtract it from your count for 3500 Hz, multiply this number by 3 dB (because each tone in the sequence is decremented in amplitude by 3 dB) and then add −4 dB.
   3. For example, say you have adjusted the volume so that you can hear the first 18 levels of the 3500 Hz tone sequence. Let's say you counted an average of 5 levels for the 100 Hz tone sequence. Your threshold for 100 Hz would then be:
      (18 − 5) × 3 − 4 dB = 35 dB
4. Graph the results on semi-log graph paper.
   1. Follow the example diagram in the Introduction and graph your own Threshold of Hearing vs. Frequency curve on semi-log graph paper.
   2. The frequency is plotted on the logarithmic scale (where the lines for each order of magnitude get closer and closer together), and threshold is plotted on the linear scale.
   3. If you can't find semi-log graph paper, you can plot threshold vs. the logarithm of the frequency.
   4. Compare your results to the standard curve in the Introduction. Compare the shapes of the curves, not the absolute numbers. (You cannot compute absolute dB levels, since we did not calibrate the absolute sound intensity of the tones played.)

Disclaimer: If your equi-loudness curve doesn't look normal, don't worry about it. Practically none of us are normal. We all deviate. Together we make up what is normal with people on both sides of the mean. In addition, there is likely a "non-flat" frequency response for the speaker or headphone set that you use, which also shows up in your result. If you suspect a hearing problem, you need to be tested by a qualified professional.

Sample data table:

Variations

• Does the threshold frequency response vary as a function of age? Measure and compare the frequency responses of at least five individuals from two or more age groups.
• How does the frequency range of greatest sensitivity compare to the normal frequency range of the human voice? Do library research to find out what the normal frequency range of the human voice is, and compare this with your results.

• For more science project ideas in this area of science, see Human Behavior Project Ideas

Credits

Andrew Olson, Ph.D., Science Buddies
Kevin Donohue, DataBeam Associate Professor of Electrical and Computer Engineering, University of Kentucky

ISO, 1961. Standard R 226: Normal equal-loudness contours for pure tones and normal threshold of hearing under free-field listening conditions. International Standards Organization, Geneva, Switzerland.

Last edit date: 2006-04-21 14:12:17