Frequency Response of the Ear

If you have an audio player configured to your Web-Page viewer, you can run a test from this web page and plot the frequency response of your ear. The test primarily serves my EE221 class so they can use this information to design a hearing-aid filter to "flatten" the frequency response of their natural ear at the threshold of hearing.

The ear has a non-flat frequency response. This means that tones played at the same volume with different frequencies can sound like they are being played at different volume levels. So you can hear some tones easier than others just based on the way the ear is made and its response to vibrations at different frequencies.

Figure 1 shows a typical equal-loudness curve at the threshold of hearing (ISO R226 (1961)) . Each frequency point on the plot represents the power required for tones at that frequency (relative to 20 micro-Newtons/meter-squared) so that each tone is heard at the same loudness.

 

Figure 1.  Threshold of hearing curve.

A similar graph can be created for your own ear by properly adjusting the volume of your audio player (the use of headphones is recommended) and playing the tone file identified by the links below. Each file contains a sequence of decreasing amplitude tones in 3 dB decrements. If you are familiar with MATLAB, you can generate your own tone sequences. I created an mfile: autest.m , which creates a tone sequence based on your own parameters for the tone sequence (see comments in mfile).



40 Hz (12 levels ~ 24 sec)

3500 Hz (25 levels ~ 32 sec)

60 Hz (12 levels ~ 24 sec)

4000 Hz (25 levels ~ 32 sec)

100 Hz (12 levels ~ 24 sec)

4500 Hz (25 levels ~ 32 sec)

200 Hz (12 levels ~ 24 sec)

5000 Hz (25 levels ~ 32 sec)

250 Hz (25 Levels ~ 32 sec)

5500 Hz (25 Levels ~32 sec)

300 Hz (25 levels ~ 32 sec)

6000 Hz (25 levels ~ 32 sec)

400 Hz (25 levels ~ 32 sec)

7000 Hz (25 levels ~ 32 sec)

500 Hz (25 levels ~ 32 sec)

8000 Hz (25 levels ~ 32 sec)

600 Hz (25 levels ~ 32 sec)

9000 Hz (25 levels ~ 32 sec)

800 Hz (25 level ~ 32 sec)

10000 Hz (25 levels ~ 32 sec)

1000 Hz (25 levels ~ 32 sec)

11000 Hz (25 levels ~ 32 sec)

1200 Hz (25 levels ~ 32 sec)

12000 Hz (25 levels ~32 sec)

2000 Hz (25 levels ~ 32 sec)

14000 Hz (25 levels ~32 sec)

2400 Hz (25 levels ~ 32 sec)

15000 Hz (25 levels ~ 32 sec)

3000 Hz (25 levels ~ 32 sec)

18000 Hz (25 levels ~ 32 sec)



To plot your own equi-loudness curve, first play the 3500 Hz sequence and adjust the volume so that you hear only about the first 20 or 21 levels in the 3500 Hz sequence. So let's say you set it so you can hear 21 levels and then silence. This means that volumes associated with levels 22, 23, 24 and 25 are below your threshold of hearing. Without changing the volume of your audio player, play each tone sequence and count the number of levels you can hear. Record this number for each frequency. When you have completed all the tone sequences, let -4 dB correspond to the level counted out for 3500 Hz (-4 dB is approximately what the threshold of hearing is the figure at 3500 Hz). Then if you subtract the count at each frequency from the count at 3500 Hz, multiply the difference by 3, and add -4 dB, you will get a series of the dB levels for your equi-loudness curve that can be compared to the threshold of hearing graph above.

For example, let's say your highest count was 21 for 3500 Hz, and for 100 Hz you counted 5 audible tone levels and for 1000 Hz you counted 18 audible tone levels. You would plot -4 dB at 3500 Hz, 3*(21-5)-4=44 dB at 100 Hz and 3*(21-18)-4=5 dB at 1000 Hz. Do this for the counts at all the tones provided, and plot these points on a semilog scale (as shown in Figure 1). See how the shape of your curve compares to the one in Figure 1. Absolute dB levels cannot be computed because the sound levels were not calibrated to absolute sound intensities. This test primarily shows your equi-loudness curve relative the most sensitive spectral range. So we compare the shapes of the curves here and not the absolute numbers.

Disclaimer: If your equi-loudness curve doesn't look normal, don't worry about it. Practically none of us match “normal,” about 50% are above and 50% below. In addition, it is likely the speaker or headphone set that you used has a "non-flat" frequency response, which also shows up in your result. If you suspect a hearing problem, you need to be tested by a qualified professional.