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The shrillness of a sound does not depend upon_____.

Answer
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Hint: Define the parameters which determine how a person can differentiate between two sounds. One of the parameters is shrillness. Define the quantity that determines a comparable difference for each of the parameters. The quantities which do not affect the shrillness are the answer.

Complete step by step answer:
There are three parameters of sound which set the basis for distinction in one sound from the other. The three parameters are loudness, shrillness and Timbre.
Loudness of a sound depends on the intensity that the sound has produced. Which depends on the amplitude or the energy with which sound has been produced. Greater the amplitude, louder is the sound.
Shrillness of a sound is the virtue of its frequency. A sound is shriller when its frequency is more.
Timbre depends on the overtones present in the sound. Timbre is the property by which two sounds may appear different even if they are equally loud and shrill.
Therefore, the shrillness of the sound only depends upon the frequency.
Thus, the answer to this question is loudness and overtones present.

Additional information:
Loudness refers to how loud or soft a sound seems to a listener. The loudness of sound is determined by the intensity of the sound waves. Intensity is a measure of the amount of energy in sound waves.
The unit of intensity is the decibel (dB). Decibels are measured on a logarithmic scale with the base 10. The equation for loudness looks similar to:
$\text{Loudness = 10lo}{{\text{g}}_{10}}\left( \dfrac{I}{{{I}_{0}}} \right)dB$ Where, $I_o$ is a constant.
That is for every 10 dB increase in the intensity of sound, loudness is 10 times greater.

Note: Shrillness is also defined as the pitch of the sound. Similarly, timbre is also known as the quality of the sound. Keep the above information in mind so that you do not get confused for example if someone asks you what pitch of a sound depends upon.