All categories

3 years ago

Sound Intensity

Mathematics

1 answer:

Tasya [4]3 years ago

4 0

Answer:

$\frac{d\beta}{dI}=\frac{10^5}{ln(10)}$

Step-by-step explanation:

We are given that a relation between the number of decibles B and the intensity of a sound I

$\beta=10log_{10}(\frac{I}{10^{-16}})$

$\beta=10(log_{10}I-(-16)log_{10}10$

By using property

$log(\frac{A}{B})=log A-log B$

$logA^b=blog A$

$Log_{10}10=1$

$\beta=10(log_{10}I+16)$

Log 10=1

We have to find the rate of change in the number of decibles when the intensity I= $10^{-4}watt/cm^2$

Differentiate w.r.t I

$\frac{d\beta}{dI}=10(\frac{1}{Iln(10)}$

$\frac{d\beta}{dI}=\frac{10}{Iln(10)}$

Substitute $I=10^{-4}$

$\frac{d\beta}{dI}=\frac{10}{10^{-4}ln(10)}=\frac{10^{1+4}}{ln(10)}=\frac{10^5}{ln(10)}$

By using property $\frac{a^x}{a^y}=a^{x-y}$

$\frac{d\beta}{dI}=\frac{10^5}{ln(10)}$

You might be interested in

y=c1e^x+c2e^−x is a two-parameter family of solutions of the second order differential equation y′′−y=0. Find a solution of the

vagabundo [1.1K]

The general form of a solution of the differential equation is already provided for us:

$y(x) = c_1 \textrm{e}^x + c_2\textrm{e}^{-x},$

where $c_1, c_2 \in \mathbb{R}$ . We now want to find a solution $y$ such that $y(-1)=3$ and $y'(-1)=-3$ . Therefore, all we need to do is find the constants $c_1$ and $c_2$ that satisfy the initial conditions. For the first condition, we have: $y(-1)=3 \iff c_1 \textrm{e}^{-1} + c_2 \textrm{e}^{-(-1)} = 3 \iff c_1\textrm{e}^{-1} + c_2\textrm{e} = 3.$

For the second condition, we need to find the derivative $y'$ first. In this case, we have:

$y'(x) = \left(c_1\textrm{e}^x + c_2\textrm{e}^{-x}\right)' = c_1\textrm{e}^x - c_2\textrm{e}^{-x}.$

Therefore:

$y'(-1) = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e}^{-(-1)} = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e} = -3.$

This means that we must solve the following system of equations:

$\begin{cases}c_1\textrm{e}^{-1} + c_2\textrm{e} = 3 \\ c_1\textrm{e}^{-1} - c_2\textrm{e} = -3\end{cases}.$

If we add the equations above, we get:

$\left(c_1\textrm{e}^{-1} + c_2\textrm{e}\right) + \left(c_1\textrm{e}^{-1} - c_2\textrm{e} \right) = 3-3 \iff 2c_1\textrm{e}^{-1} = 0 \iff c_1 = 0.$

If we now substitute $c_1 = 0$ into either of the equations in the system, we get:

$c_2 \textrm{e} = 3 \iff c_2 = \dfrac{3}{\textrm{e}} = 3\textrm{e}^{-1.}$

This means that the solution obeying the initial conditions is:

$\boxed{y(x) = 3\textrm{e}^{-1} \times \textrm{e}^{-x} = 3\textrm{e}^{-x-1}}.$

Indeed, we can see that:

$y(-1) = 3\textrm{e}^{-(-1) -1} = 3\textrm{e}^{1-1} = 3\textrm{e}^0 = 3$

$y'(x) =-3\textrm{e}^{-x-1} \implies y'(-1) = -3\textrm{e}^{-(-1)-1} = -3\textrm{e}^{1-1} = -3\textrm{e}^0 = -3,$

which do correspond to the desired initial conditions.

3 0

3 years ago

Let's talk about dora :)

yan [13]

Answer:

DORA

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

PLEASE HELP QUICKLY!!!!!!!!!!!!!!!!!!!!!!!!!!

DiKsa [7]

Answer:

He saved for 11 weeks because 7x11=77

Step-by-step explanation:

Not sure about the adding part but the subtraction part would be 77 w - 42= 35

also w = 77

8 0

3 years ago

Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are in

aleksandrvk [35]

Answer:

a. Binomial random variable (n=4, p=0.25)

b. Attached.

c. X=1

Step-by-step explanation:

This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).

a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{4}{k} 0.25^{0}\cdot0.75^{4}$

The sample space for X is {0,1,2,3,4}

The associated probabilties are:

$P(x=0) = \dbinom{4}{0} p^{0}(1-p)^{4}=1*1*0.3164=0.3164\\\\\\P(x=1) = \dbinom{4}{1} p^{1}(1-p)^{3}=4*0.25*0.4219=0.4219\\\\\\P(x=2) = \dbinom{4}{2} p^{2}(1-p)^{2}=6*0.0625*0.5625=0.2109\\\\\\P(x=3) = \dbinom{4}{3} p^{3}(1-p)^{1}=4*0.0156*0.75=0.0469\\\\\\P(x=4) = \dbinom{4}{4} p^{4}(1-p)^{0}=1*0.0039*1=0.0039\\\\\\$

b. The histogram is attached.

c. The most likely value for X is the expected value for X (E(X)).

Is calculated as:

$E(X)=np=4\cdot0.25=1$

6 0

3 years ago

PLEASE HELP 22 POINTS!

Setler79 [48]

Answer:

The answer is B -4

Step-by-step explanation:

An inverse function is a function that will “undo” anything that the original function does. For example, if a function takes a to b, then the inverse must take b to a.

5 0

4 years ago

Read 2 more answers