If one machine creates a level of 90 decibels, what decibel level would be generated by 50 of these machines? If sounds are created at random, the net intensity is found by adding the individual intensities-not the decibels. Ignore distance effects.

Question

If one machine creates a level of 90 decibels, what decibel level would be generated by 50 of these machines? If sounds are created at random, the net intensity is found by adding the individual intensities-not the decibels. Ignore distance effects.

Answer 1

add the value 10*log50 which is 16.9 db

Answer 2

Thank you for your help

Answer 3

To determine the decibel level generated by 50 of these machines, we need to understand that the intensity levels of sounds add up, not the decibel levels.

The formula to calculate the total intensity of multiple sounds is given by:

I = I1 + I2 + I3 + ... + In

Where I represents the total intensity, and I1, I2, I3, and so on, represent the individual intensities.

In this case, if one machine creates a level of 90 decibels, it does not directly provide information about its intensity. However, we can make an assumption based on the typical range of intensities for different decibel levels.

Let's assume the intensity of the sound generated by one machine corresponds to an intensity level of 10^x, where x is a value we need to determine.

The formula to convert decibels to intensity is given by:

I = 10^(dB/10)

Where I represents the intensity and dB represents the decibel level.

Substituting the given decibel level of 90, we have:

10^x = 10^(90/10)

Simplifying, we get:

10^x = 10^9

Since the exponential function is the inverse of the logarithmic function, we can solve for x by taking the logarithm (base 10) of both sides:

x = log10(10^9)

x = 9

Therefore, the intensity of the sound generated by one machine is 10^9 units.

Now, we can calculate the total intensity generated by 50 machines:

I_total = I1 + I2 + I3 + ... + I50

I_total = 10^9 + 10^9 + 10^9 + ... + 10^9 (50 times)

Simplifying:

I_total = 50 * 10^9

Finally, to determine the decibel level corresponding to this total intensity, we can use the formula to convert intensity to decibels:

dB_total = 10 * log10(I_total)

Substituting the value for I_total:

dB_total = 10 * log10(50 * 10^9)

Simplifying:

dB_total = 10 * (log10(50) + log10(10^9))

Using the properties of logarithms, we can further simplify:

dB_total = 10 * (log10(50) + 9)

Evaluating log10(50):

dB_total = 10 * (1.69897 + 9)

Simplifying:

dB_total = 10 * 10.69897

dB_total ≈ 106.9897

Therefore, the decibel level generated by 50 machines is approximately 106.9897 decibels.