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Alenkasestr [34]
3 years ago
6

Two loudspeakers are placed on a wall 2 m apart. A listener stands directly in front of one of the speakers, 81.7 m from the wal

l. The speakers are being driven by the same electric signal generated by a harmonic oscillator of frequency 4450 Hz. What is the phase difference ∆Φ between the two waves (generated by each speaker) when they reach the listener? The speed of the sound in air is 343 m/s. Answer in units of rad.
Physics
1 answer:
OverLord2011 [107]3 years ago
8 0

Answer:

The phase difference is       \Delta \phi = 1.9995 rad  

Explanation:

From the question we are told that

    The distance between the  loudspeakers is d = 2m

     The distance of the listener from the wall  D = 81.7 \ m

     The frequency of the  loudspeakers is  f = 4450Hz

      The velocity of sound is v_s = 343 m/s

     

The path difference of the sound wave that is getting to the listener is mathematically represented as

        \Delta z  =\sqrt{d^2 + D^2} -D

Substituting values

        \Delta z  =\sqrt{2^2 + 81.7^2 } -81.7

       \Delta z  =0.0245m

The phase difference is mathematically represented as

           \Delta \phi =  \frac{2 \pi}{\lambda } *  \Delta z

Where \lambda is the wavelength which is mathematically represented as

          \lambda  = \frac{v_s }{f}

substituting value  

          \lambda  = \frac{343 }{4450}

        \lambda  = 0.0770 m

Substituting value into the  equation for phase difference

      \Delta \phi =  \frac{2 * 3.142 * 0.0245}{0.0770}

      \Delta \phi = 1.9995 rad  

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