# Intensity Level of 76 trombones

• Coushander
In summary, the intensity level of 76 identical trombones, all at distance d, would be approximately 88.808 dB, calculated using the equation β = 10*log10(I/I0) and the given intensity level of 70 dB for one trombone. This is due to the fact that for each doubling of intensity, we increase 3 dB, leading to an increase in intensity level for 76 identical trombones. However, there may be slight discrepancies due to arithmetic errors.
Coushander

## Homework Statement

If the intensity level at distance d of one trombone is 70 dB, what is the intensity level of 76 identical trombones, all at distance d?

## Homework Equations

β = (10 dB) log10(I/I0)

I0= 1.0 x 10-12 W/m2

I = power/area

## The Attempt at a Solution

70db = 10db log10(I/I0)

7db = log10(I/I0)

107 = 10log10(I/I0)

107 = (I/I0)

I = 0.00001 W/m2

Then I multiplied that by 76 and put it back in the general equation to generate β = 98db, which is wrong. β = 89db.

Coushander said:

## Homework Statement

If the intensity level at distance d of one trombone is 70 dB, what is the intensity level of 76 identical trombones, all at distance d?

## Homework Equations

β = (10 dB) log10(I/I0)

I0= 1.0 x 10-12 W/m2

I = power/area

## The Attempt at a Solution

70db = 10db log10(I/I0)

7db = log10(I/I0)

107 = 10log10(I/I0)

107 = (I/I0)

I = 0.00001 W/m2

Then I multiplied that by 76 and put it back in the general equation to generate β = 98db, which is wrong. β = 89db.

Your argument seems sound, but you arithmetic must have gone astray.

For each doubling of intensity, we increase 3 dB [10*log102 = 3]

1 trombone = 70dB
2 -> 73 dB
4 -> 76 dB
8 -> 79 dB
16 -> 82 dB
32 -> 85 dB
64 -> 88 dB
128 -> 91 dB

so 89 dB seems quite possible

indeed 10*log1076 = 18.8,
so final intensity is 70 + 18.8 = 88.8, or perhaps 89 dB

[must be annoying to see it is that simple to calculate]

You're right, it was an arithmetic error.

Working it through again gave me 88.57dB this time (did it twice to make sure).

Coushander said:
You're right, it was an arithmetic error.

Working it through again gave me 88.57dB this time (did it twice to make sure).

You actually should be getting 88.808 dB. Not sure why the discrepecy? your figure is the sound of 72 trombones!

I would like to clarify that the intensity level of a sound is measured in decibels (dB) and is calculated using the equation β = (10 dB) log10(I/I0), where I is the sound intensity and I0 is the reference intensity of 1.0 x 10-12 W/m2. Therefore, the intensity level of one trombone at a distance d of 70 dB can be calculated as:

β = (10 dB) log10(I/I0)

70 dB = (10 dB) log10(I/I0)

7 = log10(I/I0)

107 = I/I0

I = 1.0 x 10-5 W/m2

Since we are dealing with 76 identical trombones, the intensity level of the combined sound can be calculated by adding the individual intensity levels using the equation β1 + β2 + ... + βn, where n is the number of identical sources. In this case, n = 76.

Therefore, the intensity level of 76 identical trombones at a distance d can be calculated as:

β = 70 dB + 70 dB + ... + 70 dB (76 times)

β = 5320 dB

However, this result is not physically meaningful as the intensity level cannot exceed 194 dB. This is due to the fact that the equation for intensity level is logarithmic and a very large number of sources can lead to a misleading result. In reality, the combined intensity level of multiple sources is always lower than the individual intensity levels.

In conclusion, the intensity level of 76 identical trombones at a distance d cannot be accurately calculated using the given information. Further measurements and calculations would be needed to determine the actual intensity level.

## 1. What is the intensity level of 76 trombones?

The intensity level of 76 trombones refers to the loudness or strength of the sound produced by 76 trombones playing together. It is measured in decibels (dB) and can vary depending on factors such as the size and quality of the instruments, the skill of the players, and the acoustics of the performance space.

## 2. How does the intensity level of 76 trombones compare to other musical instruments?

The intensity level of 76 trombones can vary, but on average, it is similar to other brass instruments such as trumpets and tubas. However, it may be slightly louder than woodwind instruments like clarinets or flutes. The intensity level can also depend on the specific type of trombone being used.

## 3. Can the intensity level of 76 trombones be dangerous to human hearing?

Yes, the intensity level of 76 trombones can reach levels that are considered dangerous to human hearing. Prolonged exposure to high intensity levels can cause hearing damage and even permanent hearing loss. It is important for musicians and audience members to protect their ears when exposed to loud music.

## 4. How is the intensity level of 76 trombones measured?

The intensity level of 76 trombones is typically measured using a decibel meter. This device measures the sound pressure level in decibels and can give an accurate reading of the intensity level of the music being produced by the trombones. It is important to calibrate the decibel meter properly for accurate results.

## 5. Can the intensity level of 76 trombones be controlled?

Yes, the intensity level of 76 trombones can be controlled by the musicians playing the instruments. By adjusting the force and speed of their playing, they can change the intensity level of the sound produced. Additionally, using mutes or adjusting the distance between players can also help control the overall intensity level of the music.

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