Solving Three Physics Problems: SIL and Sound Intensity Calculations

[spherenine]

Three homework questions. I didn't post them in the homework section because I can't even attempt them because my professor didn't even explain them well enough for me to be able to do that. I'm not looking for specific answers, but more just a simple explanation of how to do the type of problem in general. Here goes:

A clarinet plays a soft note with a SIL of 40 dB. By what factor must the intensity be increased in order to play the same note at a SIL of 70 dB.

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If the whirring of a single fan produces a SIL of 50 dB, how many identical fans would need to be operated simultaneously to make a SIL of 63 dB?

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A 100-Hz sawtooth wave and a 202-Hz sine wave are sounded simultaneously. What is the frequency of the resulting beats?

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I just need formulas, really.

 

[vanesch]

Three homework questions. I didn't post them in the homework section because I can't even attempt them because my professor didn't even explain them well enough for me to be able to do that. I'm not looking for specific answers, but more just a simple explanation of how to do the type of problem in general. Here goes:

A clarinet plays a soft note with a SIL of 40 dB. By what factor must the intensity be increased in order to play the same note at a SIL of 70 dB.

What's the relationship between a sound intensity level in dB and the intensity of the wave ?

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If the whirring of a single fan produces a SIL of 50 dB, how many identical fans would need to be operated simultaneously to make a SIL of 63 dB?

Same as previous, plus: how does the intensity increase when two incoherent sources are put together ?

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A 100-Hz sawtooth wave and a 202-Hz sine wave are sounded simultaneously. What is the frequency of the resulting beats?

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What's the relationship between the frequency of the beats and the frequencies of the composing fundamentals ?

I just need formulas, really.

I think the point of the homework was to make you recall the right formula. Everyone can put in the numbers when he/she has the formulas, that's really really not difficult. The homework wanted to see if you understood the course material well enough in order for you to pick the right formula. So giving you the formula would be doing the essence of your homework for you.

I move this to HW...

 

[m2003]

Hello,

I understand that you are struggling with these physics problems and your professor has not provided enough explanation for you to attempt them. I will do my best to provide a simple explanation of the concepts involved in solving these types of problems.

1. SIL and Sound Intensity Calculations

SIL stands for Sound Intensity Level, which is a measure of the loudness of a sound. It is measured in decibels (dB), which is a logarithmic scale. This means that a change in SIL by 10 dB represents a 10-fold change in sound intensity.

In order to solve problems involving SIL and sound intensity calculations, you will need to use the following formula:

SIL = 10 log(I/I0)

Where SIL is the sound intensity level, I is the sound intensity in watts per square meter, and I0 is the reference intensity, which is 10^-12 watts per square meter.

To solve for the factor by which the intensity must be increased to achieve a certain SIL, you can use the following formula:

Factor = 10^(SIL/10)

Where SIL is the desired sound intensity level.

2. Clarinet SIL Calculation

In this problem, you are given the SIL of a soft note played by a clarinet (40 dB) and you need to find the factor by which the intensity must be increased to achieve a SIL of 70 dB.

Using the formula above, we can set up the following equation:

70 = 10 log(I/I0)

Solving for I, we get:

I = I0 * 10^(70/10)

I = I0 * 10^7

So, the factor by which the intensity must be increased is 10^7, or 10 million.

3. Fan SIL Calculation

In this problem, you are given the SIL of a single fan (50 dB) and you need to find the number of identical fans needed to achieve a SIL of 63 dB.

Using the formula above, we can set up the following equation:

63 = 10 log(n*I/I0)

Where n is the number of identical fans.

Solving for n, we get:

n = 10^(63/10) / 10^(50/10)

n = 10^1.3 / 10^1

n = 10^0.3

So, we need approximately 2 fans to achieve a SIL of 63 dB.

4. Beats Frequency