Equal Loudness Curves (AQA A Level Physics)

On the axes below, sketch an equal loudness curve showing the normal response of a healthy ear.

Annotate the frequency axis with an appropriate scale.

Answer:

Step 1: Recall the frequency range of human hearing

• For a normal ear, the range of human hearing is 20 to 20,000 Hz

Step 2: Recall how to plot a logarithmic scale

• On a logarithmic scale, each large division on the scale represents an increase by the base of the log (usually 10) to a power that increases linearly (i.e. 10¹, 10², 10³)

• Then for each small division, instead of progressing linearly (e.g. 0, 1, 2, 3, 4...), a logarithmic scale progresses nonlinearly, but still in equal increments (e.g. 10, 20, 30, 40...)

Step 3: Label the frequency axis with a logarithmic scale

• There are 3 large divisions on the axes provided, so we should plot the frequencies between 100, 1000 and 10 000 Hz, as this range is where the ear is most sensitive

  • 10, 100 and 1000 Hz would be too low of a range

  • 1000, 10 000 and 100 000 Hz would be too large of a range

• Between the large divisions, there are 9 small divisions - there is no 'zero' on a logarithmic scale, so each small division represents increments of 100 and 1000 respectively

  

• The scale should start at 100 Hz, then 1000 Hz at the midpoint, and end at 10 000 Hz

• Between 100 Hz and 1000 Hz, each division on the scale represents 100 Hz

• Between 1000 Hz and 10 000 Hz, each division on the scale represents 1000 Hz

• Therefore, the locations of 300 Hz and 3000 Hz are two divisions from 100 Hz and 1000 Hz respectively

Step 4: Draw a U-shaped curve with the lowest point at 3000 Hz

• The equal loudness curve for a normal ear has a U-shape

• The frequency a normal ear is most sensitive to is about 3000 Hz

• Therefore, this corresponds to the quietest sound or lowest intensity level on the decibel scale

The diagram shows the equal loudness curve obtained when a patient has a hearing test at a level above the threshold of hearing.

(a) Explain how the equal loudness curve was obtained. 

(b) On the diagram draw an equal loudness curve which passes through 100 dB at a frequency of 1 kHz.

Answer:

Part (a)

Hearing test to generate the equal loudness curve:

• The patient listens to a reference sound at 1 kHz and intensity level 10 dB

• Then they listen to a sound at a different frequency and loudness

• They switch between the sound at 1 kHz and the sound at the new frequency and the loudness is adjusted until the same loudness is perceived - the value of loudness is recorded

• The process is repeated for frequencies between 20 Hz and 20 kHz

Part (b)

Equal loudness curve for 100 dB at 1000 Hz:

• The general shape should be flatter and must pass through point 100 dB at 1000 Hz

• Both curves are most sensitive at about 3000 Hz, so they both have a minimum intensity level here

An understanding of the unit 'phon' is not required in this specification but you may come across it in your revision of equal loudness curves, so it is included here to aid your understanding

The loudness of a sound in phons is defined as the intensity level in decibels of a sound at 1000 Hz that has the same loudness as the sound, i.e. a 40 dB sound at 1000 Hz has a loudness of 40 phons. From the same curve, a 100 dB sound at 10 000 Hz also has a loudness of 40 phons.

A sound source of constant output power is used to generate a sound which is measured using a sound meter. When set to the dB scale, the sound meter displayed 80 dB as the reading when the frequency of the sound was 1 kHz.

State and explain:

(a) the main differences between the dB and dBA scales.

(b) what the reading would be for a sound of frequency 1 kHz if the meter was changed to the dBA scale.

(c) what would happen to the reading on each scale if the frequency of the sound was changed to 1.5 kHz.

 Answer:

Part (a)

• The dB scale is not frequency dependent, so the output is the same at all frequencies 

• The dBA scale is frequency dependent, so threshold intensities are different for different frequencies

• Frequencies on the dBA scale are adjusted to match the response of the human ear

Part (b)

• The reading on the dBA scale would be 80 dBA as 1 kHz is the reference frequency (at the threshold of hearing)

Part (c)

• The dB reading would be 80 dB as the power is constant (and dB scale is not frequency dependent)

• The dBA reading would be more than 80 dB as the ear is more sensitive at 1.5 kHz than at 1 kHz (or 1.5 kHz has a lower threshold intensity)

Make sure you can draw the graph of intensity level in dBA against frequency - the key points to remember are

• The dB line is flat

• The dBA curve has the inverse shape to the equal loudness curve

• The dBA curve peaks at 3 kHz (frequency of maximum sensitivity)

• Both scales should have the same reading at 1 kHz (the reference frequency)