Question

In: Physics

The rule of thumb for loudness is that the power of a sound must be increaed...

The rule of thumb for loudness is that the power of a sound must be increaed by a factor of _____ to sound twice as loud.

A. 2

B. 12

C. 20

D. 10

E. 100

Expert Solution

Answer: D. 10

We tend to normally think that doubling the power would mean twice the loudness. This is not true because our ear perceives the loudness of a sound signal in a very non-linear way. When experiments were done to understand the relationship between the two, the power of the amplifier of the speaker was incresed by known values and subjects (participants) were asked how much louder did they hear the sound compared to the previous one. It was found that increasing the power 10 times is perceived as twice as loud. Such a dependency can be mathematically represented in terms of the Logarithmic function (not the natural log but log to the base 10). For example:

We can see that making the value inside Log 10 times, the answer became two times. The final expression is:

where represents reference power (generally the minimum power that our ear can perceive). The unit of Loudness is Bel (as calculated from the above formula) but a more common unit is decibel which is a smaller unit where;

1 Bel = 10 Decibels

Hence,

Loudness in Decibel =

genius_generous answered 2 years ago

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