Question

When two people sing a chorus having the same pitch and louder we are still able to distinguish their sound. Why?
Explain in detail

Answer 1

Lecture 13: More on Perception of Loudness

We have now seen that perception of loudness is not linear in how loud a sound is, but

scales roughly as a factor of 2 in perception for a factor of 10 in intensity. However, we still

have not seen how to compare,

• sounds of different frequency as well as intensity

• sounds of different duration

• sounds composed of several sine waves, such as real musical tones or simultaneous tones

from several instruments.

Let’s talk about these next.

Frequency and Loudness

Tones of the same intensity (power per area), but of different frequency, are perceived as

being of different loudness. To simplify the discussion, consider just sustained tones where

the pressure is a sine wave. If two sounds have the same intensity and their frequencies lie

between about 600 and 2000 Hertz, they will be perceived to be about the same loudness.

Outside of this range, that is not the case. For sounds near 3000 to 4000 Hertz, the ear is

extra-sensitive; these sounds are perceived as being louder than a 1000 Hertz sound of the

same intensity. At frequencies lower than 300 Hertz, the ear becomes less sensitive; sounds

with this frequency are perceived as being less loud than a sound of the same intensity and

1000 Hertz frequency. The loss of sensitivity gets bigger as one goes to lower frequencies.

Also, at very high frequencies sensitivity is again reduced.

Let us very briefly explain why each of these features is present.

• Hearing below about 300 Hertz becomes inefficient partly because the cochlea does not

respond as well here, but also largely because the transmission of the vibrations through

the ear bones becomes less efficient at low frequencies. [This is a common problem with

impedance matching: below some characteristic frequency of the impedance matcher,

it stops working efficiently. We might return to this after talking about resonance and

impedance, when we discuss brass instruments.]

• The meatus is a tube, roughly cylindrical and of a certain length. As we will see

later, such a tube has a resonant frequency, and sound waves at or near that frequency

bounce back and forth several times in the tube before leaving, giving the ear a larger

sensitivity to capture that sound. As we will see, the resonant wave length is λ = 4L

Answer 2

Why is it that the two persons sound louder than they would individually?
I would imagine that since the traverse waves generated by the two persons would randomly be louder or softer, based on the phase shift between the two sound waves. But that hypothesis is obviously untrue since in the real world a choir is clearly louder than a soloist.


This is a neat question. Did you know that adding two Sine waves of the same frequency but different phase together always produces another Sine wave? Of course you can imagine two perfectly out-of-phase Sine waves that "cancel" by adding to a line but in that case you can just imagine the result as a Sine wave with 0 amplitude.
Using gnuplot with the following commands I plotted the sum of 4 Sine waves:
a = rand(0) b = rand(0) c = rand(0) d = rand(0) plot sin(x + a * (2 * pi)) + sin(x + b * (2 * pi)) + sin(x + c * (2 * pi)) + sin(x + d * (2 * pi))