Understanding the Relationship between Amplitude & Loudness of Sound Waves

[haleycomet2]

Homework Statement

two sound waves of the same frequency have respective amplitudes of 3 units and 1 unit and are traveling in opposite directions in the same straight line.At a particular place in that line ,the resultant wave will vary in loudness.The ratio maximum loudness/minimum loudness is
answer=4/1

Homework Equations

intensity/loudness=(amplitude)^2

The Attempt at a Solution

i let the wave equation be 3sin (wt) and sin(-wt) and the resultant equation will be 3sin(wt)-sin(wt)=2sin(wt),so i think the answer should be (2/0)^2.I am doubtful whether my wave equation in opposite direction is correct.

 

[anathema]

Dear fellow scientist,

Your approach to solve this problem is correct. However, there are a few points that need clarification.

Firstly, the wave equation for sound waves should take the form of a pressure wave, not a displacement wave. So, the correct wave equations for the two sound waves would be 3cos(wt) and cos(wt) respectively, since we are considering the amplitude of the pressure wave.

Secondly, when adding two waves traveling in opposite directions, the amplitude of the resultant wave is the difference between the amplitudes of the two individual waves. In this case, the resultant wave would have an amplitude of 2 units (3 units - 1 unit).

Finally, to calculate the loudness/intensity of a sound wave, we use the formula I = (amplitude)^2. So, in this case, the maximum loudness would be (2)^2 = 4 units and the minimum loudness would be (0)^2 = 0 units. Therefore, the ratio of maximum loudness to minimum loudness would be 4/1.

I hope this clarifies your doubts and helps you in solving the problem.