Answer
a) $80\;\rm cm$
b) $100\;\rm cm$
Work Step by Step
a) At a separation distance of 20 cm, there is a constructive interference between the two waves of the two identical loudspeakers. At a separation distance of 60 cm, there is a destructive interference.
Hence, the wavelength is given by
$$\dfrac{\lambda}{2}=x_2-x_1$$
$$\lambda=2(x_2-x_1)=2(60-20)$$
$$\lambda=\color{red}{\bf 80}\;\rm cm$$
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b) Now we need to move the two speakers an extra 20 cm away from each other to get a new maximum constructive interference.
Hence, the separation distance between them is then
$$\Delta x=80+20=\color{red}{\bf 100}\;\rm cm$$
