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blondinia [14]
3 years ago
6

Suppose that the separation between two speakers A and B is 4.80 m and the speakers are vibrating in-phase. They are playing ide

ntical 134-Hz tones and the speed of sound is 343 m/s. An observer is seated at a position directly facing speaker B in such a way that his line of sight extending to B is perpendicular to the imaginary line between A and B. What is the largest possible distance between speaker B and the observer, such that he observes destructive interference
Physics
1 answer:
Hatshy [7]3 years ago
4 0

Answer:

X=8.44m

Explanation:

From the question we are told that

Distance b/w A&B x=4.80m

Frequency f=134Hz

Sound speed v=343m/s

Generally the equation for wavelength is mathematically given as

\lambda=v/f

\lambda/2=1/2*v/f

\lambda/2=1/2*\frac{343}{135}

\lambda/2=1.27037037

Generally the destructive interference X is mathematically given by

\sqrt{4.8^2 +X^2} -X=1.27037037\\

23.04+BC^2=X^2+1.613+2.54*X

Therefore the destructive interference is

X=8.44m

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       The near point with the glasses on is n_g =25 \ cm

     

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         Object distance would be u = -25 \ cm

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              \frac{1}{f} =  \frac{1}{v}  -  \frac{1}{u}

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              \frac{1}{f} =  \frac{1}{-15}  -  \frac{1}{-25}

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               f =  - \frac{75}{2} * \frac{1}{100}

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                P  = \frac{1}{f}

Substituting values

                 P = -  \frac{200}{75}  m

                 P = - 2.667 \ D

   

From these parameter we can see that with the glass on that for far  point the

         Object distance would be u_f = - \infty \ cm

          Image distance would be  v_f =  -20  \ cm

To obtain the focal length of the lens we would apply the lens formula which is mathematically represented as

                    \frac{1}{f_f} =  \frac{1}{v_f}  -  \frac{1}{u_f}

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                  \frac{1}{f} =  \frac{1}{-20}  -  \frac{1}{- \infty}

                 \frac{1}{f} =  \frac{1}{-20}  -  0      

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converting to  meters

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This implies that the range of powers of the lens in his glass is

                  - 5 \ D \le P \le - 2.667\  D

   

               

               

           

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