Precal Blog

On Friday in class, Mr. B gave us a problem to start with.  It was as follows:

How many times more powerful is the sound of a chainsaw (110 db) than the noise generated by a vacuum cleaner (sound intensity 10^-1)?

Using the equation we know for finding the intensity of a sound, we can set up the equation:

110 = 10 * log (I/Io)

Since we know that the relative intensity (the sound of a whisper) is 10^-12, we can fill that in for Io, giving us this:

110 = 10* log (I/10^-12)

Next, we can divide by 10 on both sides to simplify:

11 = log(I/10^-12)

Here is the important part….Since the magnitude (11) is the number of the exponent of the log function, we know that (I/Io) needs to equal 10^11.

Next, we can evaluate for the vacuum cleaner with a similar process.

Since the intensity is is 10^-1, and the relative intensity is still 10^-12, you still get an answer of 10^11.

So, they are the same.

We also touched on the point that when making a number line for these values, the evaluated log function (such as magnitude in the earthquake example), the points will directly correspond to such points on a number line showing intensity. Hence, it is vital to make sure that the number line is scaled in a uniform manner.

Lastly, we found that logx=y is a logarithmic function, while 10^y = x is an exponential function.  This is why we have been studying logarithmic functions; they have a close relationship with exponential functions.

The next scribe will be…..named later, because I don’t have the list of people who have yet to go twice.  This is my third time, just so all of you know, so don’t pick me again.  EVER.

One love,

Nathan