derive relation for the energy contained in a unit volume of medium transfering waves and intensity at a point of the medium and hence show that intensity is proportional to the square of amplitude.
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The amplitude of a sound wave can be quantified in at least three ways:
by measuring the maximum change in position of the particles that make up the medium (the maximum particle displacement)by measuring the maximum change in density of the mediumby measuring the maximum change in pressure (the maximum gauge pressure)
Measuring displacement might as well be impossible. For typical sound waves, the maximum displacement of the molecules in the air is only a hundred or a thousand times larger than the molecules themselves — and what technologies are there for tracking individual molecules anyway?
Density fluctuations are equally minuscule and short lived. (The period of sound waves is typically measured in milliseconds.) There are some optical techniques that make it possible to see the intense compressions are rarefactions associated with shock waves in air, but this will be dealt with in another section of this book.
Pressure fluctuations caused by sound waves are much easier to measure. Animals (including humans) have been doing it for several hundred million years with devices called ears. Humans have also been doing it electromechanically for about a hundred years with devices called microphones.
In any case, the results of such measurements are rarely ever reported. Instead, amplitude measurements are almost always used as the raw data in some computation. When done by an electronic circuit (like the circuits in a level meter) the resulting value is called intensity. When done by a neuronal circuit (like the circuits in your brain) the resulting sensation is called loudness.
The intensity of a sound wave is a combination of its rate and density of energy transfer. It is an objective quantity associated with a wave. Loudness is a perceptual response to the physical property of intensity. It is a subjective quality associated with a wave and is a bit more complex. As a general rule the larger the amplitude, the greater the intensity, the louder the sound. Sound waves with large amplitudes are said to be "loud". Sound waves with small amplitudes are said to be "quiet" or "soft". (The word "low" is sometimes also used to mean quiet, but this should be avoided. Use "low" to describe sounds that are low in frequency.) Loudness will be discussed at the end of this section.
By definition, the intensity (I) of any wave is the time-averaged power (⟨P⟩) it transfers per area (A) through some region of space. The traditional way to indicate the time-averaged value of a varying quantity is to enclose it in angle brackets ⟨⟩ . These look similar to the greater and less than symbols but they are taller and less pointy. That gives us an equation that looks like this…
I = ⟨P⟩A
The SI unit of power is the watt, the SI unit of area is the square meter, so the SI unit of intensity is the watt per square meter — a unit that has no special name.
⎡
⎣W = W⎤
⎦m2m2
by measuring the maximum change in position of the particles that make up the medium (the maximum particle displacement)by measuring the maximum change in density of the mediumby measuring the maximum change in pressure (the maximum gauge pressure)
Measuring displacement might as well be impossible. For typical sound waves, the maximum displacement of the molecules in the air is only a hundred or a thousand times larger than the molecules themselves — and what technologies are there for tracking individual molecules anyway?
Density fluctuations are equally minuscule and short lived. (The period of sound waves is typically measured in milliseconds.) There are some optical techniques that make it possible to see the intense compressions are rarefactions associated with shock waves in air, but this will be dealt with in another section of this book.
Pressure fluctuations caused by sound waves are much easier to measure. Animals (including humans) have been doing it for several hundred million years with devices called ears. Humans have also been doing it electromechanically for about a hundred years with devices called microphones.
In any case, the results of such measurements are rarely ever reported. Instead, amplitude measurements are almost always used as the raw data in some computation. When done by an electronic circuit (like the circuits in a level meter) the resulting value is called intensity. When done by a neuronal circuit (like the circuits in your brain) the resulting sensation is called loudness.
The intensity of a sound wave is a combination of its rate and density of energy transfer. It is an objective quantity associated with a wave. Loudness is a perceptual response to the physical property of intensity. It is a subjective quality associated with a wave and is a bit more complex. As a general rule the larger the amplitude, the greater the intensity, the louder the sound. Sound waves with large amplitudes are said to be "loud". Sound waves with small amplitudes are said to be "quiet" or "soft". (The word "low" is sometimes also used to mean quiet, but this should be avoided. Use "low" to describe sounds that are low in frequency.) Loudness will be discussed at the end of this section.
By definition, the intensity (I) of any wave is the time-averaged power (⟨P⟩) it transfers per area (A) through some region of space. The traditional way to indicate the time-averaged value of a varying quantity is to enclose it in angle brackets ⟨⟩ . These look similar to the greater and less than symbols but they are taller and less pointy. That gives us an equation that looks like this…
I = ⟨P⟩A
The SI unit of power is the watt, the SI unit of area is the square meter, so the SI unit of intensity is the watt per square meter — a unit that has no special name.
⎡
⎣W = W⎤
⎦m2m2
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