Answer
See the detailed answer below.
Work Step by Step
We know that the two loudspeakers emit identical in-phase waves.
We also know that the net amplitude is given by
$$A=\left|2a\cos\left(\frac{\Delta \phi}{2}\right) \right|$$
where $\Delta \phi=\dfrac{2\pi \Delta r}{\lambda}$
So that
$$A=\left|2a\cos\left(\frac{ \pi \Delta r}{ \lambda}\right) \right|$$
where $\lambda=2$ m
$$A=\left|2a\cos\left(\frac{ \pi \Delta r}{ 2}\right) \right|\tag 1$$
Now we will use (1) to find $A$ interms of $a$ at the given points.
At (0,0), $\Delta r=0$, so
$$A_{(0,0)}=\left|2a\cos\left(\frac{ \pi (0)}{ 2}\right) \right| =2a\cos(0)$$
$$\boxed{A_{(0,0)}=\color{red}{\bf 2\;}a}$$
At (0,0.5), $\Delta r =3.91-3.35=\bf 0.55$ m, so
$$A_{(0,0.5)}=\left|2a\cos\left(\frac{ \pi (0.55)}{ 2}\right) \right| $$
$$\boxed{A_{(0,0.5)}=\color{red}{\bf 1.3\;}a}$$
At (0,1), $\Delta r =4.24-3.16=\bf 1.08$ m, so
$$A_{(0,1)}=\left|2a\cos\left(\frac{ \pi (1.08)}{ 2}\right) \right| $$
$$\boxed{A_{(0,1)}=\color{red}{\bf 0.25\;}a}$$
At (0,1.5), $\Delta r =4.61-3.04=\bf 1.57$ m, so
$$A_{(0,1.5)}=\left|2a\cos\left(\frac{ \pi (1.57)}{ 2}\right) \right| $$
$$\boxed{A_{(0,1.5)}=\color{red}{\bf 1.56\;}a}$$
At (0,2), $\Delta r =5-3=\bf 2$ m, so
$$A_{(0,1.5)}=\left|2a\cos\left(\frac{ \pi (2)}{ 2}\right) \right| $$
$$\boxed{A_{(0,1.5)}=\color{red}{\bf 2\;}a}$$
