Answer
a) $80\;\rm cm$
b) $\frac{3}{4}\pi$
c) $0.77a$
Work Step by Step
$$\bf a)$$ We know that both speakers are emitting sound waves of the same frequency, so to move from destructive interference to constructive interference, the separation distance between them is given by
$$\Delta x=\frac{1}{2}\lambda$$
Hence,
$$\lambda=2\Delta x=2(40)$$
Noting that $\Delta x=10+30=40$ cm,
$$\lambda=\color{red}{\bf80}\;\rm cm$$
$$\bf b)$$ We have a destructive interference when the separation distance between them is 10 cm, so
$$\Delta \phi=\dfrac{2\pi \Delta x}{\lambda}+\Delta \phi_0$$
where at 10 cm $\Delta \phi=\pi$
$$\pi=\dfrac{2\pi \Delta x}{\lambda}+\Delta \phi_0$$
$$\Delta \phi_0=\pi-\dfrac{2\pi (10)}{80}$$
$$\Delta \phi_0=\color{red}{\bf \frac{3}{4}\pi}$$
$$\bf c)$$ When two speakers are now placed side by side, the net amplitude is then given by
$$A=2a\cos\left[ \dfrac{\Delta \phi}{2} \right]$$
Hence,
$$A=2a\cos\left[ \dfrac{\frac{3}{4}\pi}{2} \right]$$
$$A=\color{red}{\bf 0.77}a$$
