Calculating Relative Maximum for Sound Waves from Speakers Separated by .7m

[sun]

Homework Statement

A pair of speakers separatd by .700m are driven by the same oscillator at a frequency of 690Hz. An observer originally positioned at one of the speakers begins to walk along a line perpindicular to the line joining the speakers. How far mus the observer walk before reaching a relative maximum in intensity

Homework Equations

v(air)=345m/s

r2-r1=n(lambda)

The Attempt at a Solution

How do i figure out the r values when only one side is given? I know i should use the pythagorean theorem here. I also know a relative maximum is constructive interference so i will use a full integer for n. r2-r2=1(lambda). I'm not sure what I'm missing here.

i have:
f=690Hz
lambda=.5m
T=.0015s

suggestions would be appreciated.
thanks

 

[rl.bhat]

Let A an B are the positions of speakers and C is the position of the observer. When observer listenes maximum intensity, the path difference CB -CA = lamda = 0.5 m. According to pythagorean theorem CB^2 - CA^2 = AB^2. Solve these equations and find the distance CA of the observer.

 

[ogb p]

I would approach this problem by first understanding the concept of constructive interference and how it relates to sound waves from two sources. In this case, the two sources are the speakers separated by 0.7m, and the observer walking along a perpendicular line.

To find the distance at which the observer will experience a relative maximum in intensity, we can use the equation r2-r1=n(lambda), where r2 is the distance from the second speaker to the observer, r1 is the distance from the first speaker to the observer, n is an integer representing the number of wavelengths, and lambda is the wavelength of the sound wave.

Since the frequency of the sound wave is 690Hz, we can use the equation v(air)=f(lambda) to find the wavelength, where v(air) is the speed of sound in air (345m/s) and f is the frequency. This gives us a wavelength of approximately 0.5m.

Now, we can plug in the values we have into the equation r2-r1=n(lambda) and solve for r2. Since we want to find the distance at which the observer reaches a relative maximum, we can let n=1. This means that r2-r1=1(lambda), or r2-r1=0.5m.

We also know that r2-r1=0.7m, as given in the problem. So, we can set up the equation 0.7m=0.5m, and solve for r2. This gives us a value of r2=1.2m.

Therefore, the observer must walk 1.2m from the first speaker to reach a relative maximum in intensity. This distance can also be found by using the Pythagorean theorem, where the hypotenuse (r2) is equal to the square root of the sum of the squares of the two sides (r1 and 0.7m).

In conclusion, by understanding the concepts of constructive interference and using relevant equations, we can calculate the distance at which the observer will experience a relative maximum in intensity while walking along a perpendicular line from two speakers separated by 0.7m.