I'm not sure how to go about answering this question... I have all these equations and none seem to apply. The question is:
If you have two speakers on opposite sides of a concert stage producing identical sound waves with a wavelength of .8m. If you consider only the direct waves coming straight from the speakers (neglecting waves that are reflected from the ceiling, walls, etc) With only one speaker on at a time, at some point in the audience, one speaker has a pressure amplitude of 10 N/m^2, and the other speaker has pressure amplitude of 7 N/m^2. The point in the audience is .4 m farther from one speaker than the other. What is the amplitude of the pressure oscillations with both speakers on?
Thanks for the help!
The answer as I see it...
The difference of the two speaker volumns plus the decay of the transverse wave passing to the audience, that is without the exterraneous sound waves fooling the ears.
Sound is movement of air.
In a vacuum, there is no sound.
Air is like water.
When 2 equal waves slap together, they cancel, or provide the difference as in Life in the wilderness....Only the strong survive.
w a 1 w t f at yah WHO!{: Peter
To answer this question, you need to understand the concept of superposition of waves. When two waves with the same frequency and nearly the same amplitude meet at a point, their individual displacements add up to create a resultant displacement at that point.
In this case, the two speakers are producing identical sound waves with a wavelength of 0.8 m. The point in the audience is 0.4 m closer to one speaker than the other. The pressure amplitude from one speaker is 10 N/m^2, and from the other speaker, it is 7 N/m^2.
To find the amplitude of the pressure oscillations with both speakers on, you need to find the resultant pressure amplitude at that specific point. Here's how you can go about it:
1. Identify the two sources of sound waves (speakers) and the point in the audience where you want to calculate the resultant pressure amplitude.
2. Use the formula for pressure amplitude: Pressure amplitude (A) = 2πfρvA, where f is the frequency of the wave, ρ is the density of the medium (air in this case), v is the speed of sound, and A is the amplitude of the wave.
3. Calculate the wavelength (λ) using the formula: λ = v/f, where v is the speed of sound and f is the frequency of the wave.
4. Determine the phase difference (Δφ) between the two waves at the point in the audience. The phase difference depends on the path length difference (ΔL) and wavelength (λ) and can be found using the formula: Δφ = 2π(ΔL/λ).
5. Calculate the resultant pressure amplitude (Ar) using the formula for superposition of waves: Ar = √((A1^2) + (A2^2) + 2A1A2cos(Δφ)), where A1 and A2 are the pressure amplitudes from the two speakers and Δφ is the phase difference.
6. Substitute the given values into the equations and calculate the resultant pressure amplitude (Ar).
By following these steps, you should be able to find the amplitude of the pressure oscillations with both speakers on.