Can the Firecracker Be Heard?

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In summary, the decibel scale is a logarithmic scale used to measure the intensity of sound waves. It is calculated using the formula beta = 10log[I/I_0], where I_0 is a reference intensity. To convert intensity to dB, I_0 is taken to be 10^{-12}W/m^2. To find the intensity at a new distance, we can subtract the change in dB appropriate to the ratio of the new distance to the reference distance. In the conversation, the question is asked about the intensity of a firecracker at a distance of 100 m from a family house. To find this intensity, we can replace I_0 with the intensity at the reference distance and I with the
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minidee
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Can the Firecracker Be Heard?
Introduction: The decibel scale is logarithmic in intensity:

beta = 10log[I/I_0]
In this formula, I_0 is a reference intensity. To convert the intensity of sound waves from SI units to dB, I_0 is taken to be 10^{-12}W/m^2.

Once you know the intensity of a source in dB as measured at some reference distance, the intensity at a new distance can be found by subtracting the change in dB appropriate to the ratio of the new distance to the reference distance.

The change in dB corresponding to the change in distance may be found by replacing I_0 in the formula given here with the intensity at the reference distance and replacing I with the intensity at the new distance.

We apply the dB scale to a small firecracker that has an intensity of 140 dB at a distance of 1 m.


a.) The question asks: A child sets off the firecracker at a distance of 100 m from the family house. What is the sound intensity beta_100 at the house?
Express the sound intensity in decibels.


b.) Will the firecracker sound louder than the parents' conversation?

Please help! Quite lost!
 
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  • #2
I got I_1 = 10^2. What to do next?!
 
  • #3




Hello! I can provide some clarification on the questions you have regarding the sound intensity of a firecracker and its comparison to a conversation.

a.) To answer this question, we can use the formula provided in the introduction:

beta = 10log[I/I_0]

We know that the intensity of the firecracker at a distance of 1 m is 140 dB. Using this as our reference intensity (I_0), we can find the intensity at a new distance of 100 m by substituting the values into the formula:

beta_100 = 10log[I/10^{-12}] = 10log[10^{14}] = 10(14) = 140 dB

Therefore, the sound intensity of the firecracker at a distance of 100 m is also 140 dB. This means that the firecracker will still be heard at the family house, but it will not be any louder than it was at a distance of 1 m.

b.) In terms of sound intensity, a conversation between parents typically ranges from 60-70 dB. This means that the firecracker, at a distance of 100 m, will be significantly louder than their conversation. However, the perception of loudness also depends on factors such as frequency and personal sensitivity to sound. So, while the firecracker may technically have a higher sound intensity, it may not necessarily sound louder to the parents if they are not particularly sensitive to loud sounds.

I hope this helps to clarify your understanding! Let me know if you have any further questions.
 

1. Can the sound of a firecracker be heard from far away?

Yes, the sound of a firecracker can be heard from far away. The loudness of the sound depends on the distance between the firecracker and the person hearing it, as well as the type and size of the firecracker.

2. How far away can a firecracker's sound be heard?

The sound of a firecracker can be heard up to a few miles away, depending on its size and the surrounding environment. However, the sound will become softer and less distinct the farther away you are from the firecracker.

3. Can the sound of a firecracker damage my hearing?

Yes, the sound of a firecracker can potentially damage your hearing if it is close enough and loud enough. It is important to always wear ear protection when handling or being near firecrackers to prevent any potential hearing damage.

4. Why are some firecrackers louder than others?

The loudness of a firecracker depends on its size, design, and the amount of explosive material inside. Firecrackers with more explosive material will create a louder sound, while smaller firecrackers will be quieter.

5. Can the sound of a firecracker scare or harm animals?

Yes, the loud sound of a firecracker can be frightening and potentially harmful to animals, especially those with sensitive hearing. It is important to use firecrackers responsibly and away from areas with a lot of wildlife present.

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