Use equations $(1\mathrm{.}1),(1\mathrm{.}2),$ and $(1\mathrm{.}3)$ to determine the linear density of a string $()$ if a standing wave is observed to have tension $(T),$ string length $(L),$ harmonic number $($i$.$e$.,$ number of anti$-$nodes, $n),$ and frequency $(f).$

$(1\mathrm{.}1)L=n\frac{}{2}$

$(1\mathrm{.}2)v=f=>\frac{}{f}$

$(1\mathrm{.}3)v=\sqrt[\phantom{2}]{\frac{T}{}}$

The sound sources shown to the right are synchronized.

a$)$ Which two points have destructive interference?

b$)$ Is the amplitude necessarily zero at those points? If not, why?