4.) Two loudspeakers emit sound waves along the x -axis. The sound has maximum i

Question

4.) Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 17 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 51 cm .

a.) What is the wavelength of the sound? Express your answer to two significant figures and include the appropriate units.

b.) If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum? Express your answer with the appropriate units.

Explanation / Answer

Sol:

a) a separation of 17cm between the speakers leads to maximum intensity on the x axis, but a separation of 51cm leads to zero to zero intensity , that is

the waves are in phase x1 = 17cm

but out of phase when x2 = 51cm

thus

x2 -x1 = /2

= 2( x2 -x1) = 2 ( 51cm- 17cm) = 68cm

b) if the distance betwen th espeakers con tinues to increase the intensity will again be a maxium when the separation between the speakers that produces a maxiumum has increased by one wave length that is when the separation between the speakers is 17cm+ 51cm = 68cm.

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