Question

9. Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm. (a) What is the wavelength of the sound? (b) If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?

Answer 1

a) a separation of 20cm between the speakers leads to maximum intensity on the x axis,

but a separation of 60cm leads to zero to zero intensity ,

that is the waves are in phase delta(x1) = 20cm

but out of phase when delta(x2) = 60cm

thus

Delta(x2)-Delta(x1) = lemda/2

lemda = 2(Delta(x2)-Delta(x1))

= 2 ( 60cm- 20cm) = 80cm

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 20cm+ 80cm = 100cm