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 wall. 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.

The phase difference is        

Explanation:

From the question we are told that

    The distance between the  loudspeakers is

     The distance of the listener from the wall  

     The frequency of the  loudspeakers is  

      The velocity of sound is

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

Substituting values

The phase difference is mathematically represented as

            =  

Where is the wavelength which is mathematically represented as

substituting value  

Substituting value into the  equation for phase difference

      =  

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

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