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Q.62PE

Expert-verified
Found in: Page 630

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# What sound intensity levels must sounds of frequencies $${\rm{60 Hz}}$$, $${\rm{3000 Hz}}$$, and $${\rm{8000 Hz}}$$ have to have the same loudness as a $${\rm{40 dB}}$$ sound of frequency $${\rm{1000 Hz}}$$ (that is, to have a loudness of $${\rm{40 phons}}$$)?

For $$60{\rm{ }}Hz$$, $$3000{\rm{ }}Hz$$, $$8000{\rm{ }}Hz$$ frequencies, sound intensity levels will be $${\rm{70 dB}}$$, $${\rm{50 dB}}$$ , $${\rm{40 dB}}$$ respectively.

See the step by step solution

## Step 1: 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.

## Step 2: 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.

## Step 3: Analysis of this figure

Here the points that are crossings of vertical lines and $$40{\rm{ }}phon$$ curve

Now make horizontal lines corresponding to these points that are crossings of vertical lines and a $$40{\rm{ }}phon$$ curve, these horizontal lines will meet on the y-axis at some value of sound level.

Let’s see these lines one by one:

For $$60{\rm{ }}Hz$$ frequency, horizontal line cut y-axis around $${\rm{70 dB}}$$.

For $$3000{\rm{ }}Hz$$ frequency, horizontal line cut y-axis around $${\rm{50 dB}}$$.

For $$8000{\rm{ }}Hz$$ frequency, horizontal line cut y-axis around $${\rm{40 dB}}$$.