Two identical loudspeakers separated by distance d emit 200Hz sound waves along the x-axis. As you walk along the axis, away from the speake

Question

Two identical loudspeakers separated by distance d emit 200Hz sound waves along the x-axis. As you walk along the axis, away from the speakers, you don’t hear anything even though both speakers are on.What are the three lowest possible values for d? Assume a sound speed of 340m/s.

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Yến Oanh 4 years 2021-09-04T02:00:02+00:00 1 Answers 13 views 0

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    2021-09-04T02:01:20+00:00

    Answer:

    The three lowest possible values for d are 0.85 m, 2.55 m and 4.25 m.

    Explanation:

    Given that,

    Distance = d

    Frequency = 200 Hz

    Speed of sound = 340 m/s

    We need to calculate the wave length

    Using formula of frequency

    f= \dfrac{v}{\lambda}

    \lambda=\dfrac{v}{f}

    Put the value into the formula

    \lambda=\dfrac{340}{200}

    \lambda=1.7\ m

    We need to calculate the three lowest possible values for d

    Using formula of destructive interference

    \Delta\phi=2\pi\dfrac{\Delta x}{\lambda}

    2\pi\dfrac{\Delta x}{\lambda}=(m+\dfrac{1}{2})2\pi

    Where, \Delta x = distance

    Put the value into the formula

    For m = 0,

    \dfrac{\Delta x}{1.7}=(0+\dfrac{1}{2})

    \Delta x=\dfrac{1.7}{2}

    \Delta x=0.85\ m

    For m =1 ,

    \dfrac{\Delta x}{1.7}=(1+\dfrac{1}{2})

    \Delta x=\dfrac{1.7\times3}{2}

    \Delta x=2.55\ m

    For m=2,

    \dfrac{\Delta x}{1.7}=(2+\dfrac{1}{2})

    \Delta x=\dfrac{1.7\times5}{2}

    \Delta x=4.25\ m

    Hence, The three lowest possible values for d are 0.85 m, 2.55 m and 4.25 m.

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