Question

What is the approximate sound intensity level in decibels of a $600\mathrm{H}\mathrm{z}$ tone if it has a loudness of $20\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{n}\mathrm{s}$? If it has a loudness of $70\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{n}\mathrm{s}$?

Short answer

For $600Hz$frequency, $20phons$ loudness and for $600Hz$ frequency,$70phons$loudness, the intensity level will be $23dB$ and $72dB$ respectively.

Step-by-step solution

A concept

The greater the amplitude, the louder and more intense the sound.

Intensity is the number of incident photons per second per unit area (more precisely, it is energy per unit area per unit time), while frequency refers to the frequency of the photon when referred to as a wave, which is the number of waves in a second.

Figure for sound level, intensity, and loudness at given frequencies

First, make a vertical line for all given frequencies and draw a horizontal line corresponding to these vertical lines then we will get our sound intensity levels in $dB$ as shown in the figure.

Analysis of figure

Here the points that are crossings of vertical lines and $20phons$,$70phons$ curves.

Now make horizontal lines corresponding to these points that are crossings of vertical lines and$20phons$,$70phons$ curves, these horizontal lines will meet on the y-axis at some value of sound level.

Let’s see these lines one by one:

For$600Hz$frequency,$20phons$loudness - horizontal line cut y-axis around$23dB$.

For$600Hz$frequency,$70phons$ loudness- horizontal line cut y-axis around$72dB$.