MCQ about intensity of sound waves (formula manipulation)

In summary, the conversation discusses the relationship between intensity (I) and amplitude (A) in the equation I=k/x^2. The constant of proportionality, k, does not need to be calculated and can be represented as Ax=k. At point P, A and x are given, and at point Q, x is double that of point P. Therefore, A at point Q is half of A at point P.
  • #1
Originaltitle
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Homework Statement



jts37a.jpg


Homework Equations



The equation that is already given + (maybe) I is proportional to A2f2.

The Attempt at a Solution



I took the square root of 8, 8 being the Amplitude and I being proportional to the square of A. (I make the constant of proportionality 1). That's not the answer.
 
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  • #2
Originaltitle said:

Homework Statement



[ IMG]http://i49.tinypic.com/jts37a.jpg[/PLAIN]

Homework Equations



The equation that is already given + (maybe) I is proportional to A2f2.

The Attempt at a Solution



I took the square root of 8, 8 being the Amplitude and I being proportional to the square of A. (I make the constant of proportionality 1). That's not the answer.
If [itex]\ \displaystyle I\propto\frac{1}{x^2}\,,\ [/itex] then [itex]\ \displaystyle I=\frac{k}{x^2}\,,\ [/itex] where k is the constant of proportionality.

This means that [itex]I\cdot x^2=k\,,\ \text{ a constant}\ .[/itex]

Added in Edit:

This is wrong. See correct response below.
 

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  • #3
Obviously, but we can't find k here because we don't have a numerical value for x OR I.
 
  • #4
You don't need to calculate k.

At point P, we have I=k/r^2
Write a similar expression for the intensity at Q and compare it with the above expression.
 
  • #5
You are given an amplitude, A, at point P.

Also, [itex]\ \displaystyle I\propto\frac{1}{x^2}\,,\ [/itex] and [itex]\ \displaystyle I\propto{A^2}\ .\ [/itex] This means that [itex]\ \displaystyle A\propto\frac{1}{x}\,,\ [/itex] assuming they're both positive. Therefore, Ax = k, where k is some constant.

You don't need a numerical result for k.

Ax at P

is equal to

Ax at Q .
@ P, A = 8μm and x = r .

@ Q, x = 2r , what is A ?
 
  • #6
A is inversely proportional to x. So if A is doubled, x will be two times less. So if A at x is 8, A at 2x will be 8/2 which is 4.

Thanks!
 

1. What is the formula for calculating the intensity of sound waves?

The formula for calculating the intensity of sound waves is: I = P/A, where I is intensity, P is power, and A is the area of the sound wave.

2. How does manipulating the formula for intensity affect the resulting value?

Manipulating the formula for intensity will change the resulting value depending on which variable is being adjusted. For example, increasing the power P will result in a higher intensity value, while decreasing the area A will result in a lower intensity value.

3. Can the intensity of sound waves be measured in different units?

Yes, the intensity of sound waves can be measured in different units such as decibels (dB) or watts per square meter (W/m2). However, these units are often converted to the standard unit of watts per square meter for consistency.

4. How does distance affect the intensity of sound waves?

The intensity of sound waves decreases as distance from the source increases. This is because the same amount of energy is spread out over a larger area, resulting in a lower intensity value. The relationship between distance and intensity is inverse, meaning as distance increases, intensity decreases.

5. Are there any limitations to the formula for calculating intensity of sound waves?

Yes, the formula for calculating intensity of sound waves assumes that the sound is spreading out uniformly in all directions and that there are no obstructions or reflections that could affect the measurement. In reality, these factors can impact the actual intensity of sound waves in a given environment.

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