# How Do Decibels Determine Perceived Loudness and Amplifier Gain?

• leospyder
In summary, the question is asking for the sound level of a 6000 Hz tone to be equivalent to a 100 Hz tone with a 50 dB sound level. The second question involves finding the gain of a stereo amplifier in decibels, which can be calculated by dividing the output power by the input power and taking the log10 of the result.
leospyder
Can someone help me with the following questions (I have no idea where to begin in either case). There are no questions that follow these same types of concepts in the book problems.

1) A 6000 Hz tone must have what sound level to seem as loud as a 100
Hz tone that has a 50 dB sound level?

2) In audio and communications systems, the gain, denoted by b, in
decibels is defined as

$$\beta = (P_{out}/P_{in})$$

where $$P_{in}$$ is the power input and $$P_{out}$$
is the power output. Assume a particular stereo amplifier will put out 150 W of
power for an input of 1 mW. What is its gain in dB?

Last edited:
1)http://www.phys.unsw.edu.au/~jw/dB.html
look at the chart under "Loudness, phons and sones". All the dots on any curve are combinations of frequency with corresponding intensity have the same loudness. So you need to find on which curve (100Hz, 50dB) is, and see where the 6000Hz line intersects that curve.
2) Just divide the output power by the input power

## 1. What is a decibel?

A decibel (dB) is a unit used to measure the intensity or loudness of a sound. It is a logarithmic scale and is based on the ratio of the sound pressure level to a reference level.

## 2. How is sound level measured?

Sound level is measured using a device called a sound level meter. It measures the sound pressure level in decibels (dB) and displays the readings on a scale. The meter is usually calibrated to measure the sound level in a specific frequency range.

## 3. What is the range of decibel levels for common sounds?

The range of decibel levels for common sounds can vary greatly. Some examples include a whisper at 20dB, a normal conversation at 60dB, a lawnmower at 90dB, and a jet engine at 140dB. Sounds above 85dB can potentially cause hearing damage with prolonged exposure.

## 4. How does distance affect sound levels?

As sound travels, it spreads out and becomes less intense. This means that the further you are from the source of the sound, the lower the sound level will be. The inverse square law states that the sound level decreases by 6dB for every doubling of distance from the source.

## 5. Can sound levels affect human health?

Yes, sound levels can have both positive and negative effects on human health. Exposure to high levels of sound can cause hearing loss and other health issues such as stress, anxiety, and sleep disturbance. On the other hand, certain sounds at appropriate levels can have therapeutic effects on the body and mind.

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