91影视

Constructive interference occurs when the difference of the distances of each source from point P is an integer number of wavelengths. The interference is destructive when this difference of path lengths is a half integer number of wavelengths.

The wavelength is,

$\mathrm{v}=\mathrm{位蹿}$

where v is the wave velocity, f is the frequency and $位$is the wavelength of the wave.

role="math" localid="1655808613255"

The value of $x$ ranges from 0 to L, where $L=2.00m$is the distance between the speakers.

The difference in path length is

$\begin{array}{c}螖l=(L鈭�x)鈭�x\\ =L鈭�2x\\ x=(L鈭�螖l)/2\end{array}$

destructive interference occurs for path difference $\mathrm{螖濒}=(\mathrm{n}+(1/2\left)\right)\mathrm{位}$and constructive interference for $\mathrm{螖濒}=\mathrm{苍位}$.

(a) Destructive interference: $\mathrm{n}=0\mathrm{gives}\mathrm{螖濒}=0.835\text{鈥尘}\mathrm{andx}=0.58\text{鈥尘}.$

And at $\mathrm{n}=-1\text{鈥塯颈惫别蝉}\mathrm{螖濒}=-0.835\text{鈥尘}\mathrm{andx}=1.42\text{鈥尘.}$

For any other value of $n$, P will not lie between the speakers.

(b)Constructive interference: $\mathrm{n}=0\text{鈥塯颈惫别蝉}\mathrm{螖濒}=0\text{鈥尘and}\mathrm{x}=1.00\text{鈥尘}.$

And at$\mathrm{n}=1\text{gives}\mathrm{螖濒}=1.67\text{鈥尘and}\mathrm{x}=0.17\text{鈥尘}.$

At $\mathrm{n}=-1\text{鈥塯颈惫别蝉}\mathrm{螖濒}=-1.67\text{鈥尘and}\mathrm{x}=1.83\text{鈥尘.}$

For any other value of $n$, P will not lie between the speakers

(c)Treating the speakers as point sources is a poor approximation for these dimensions, and sound reaches the given points after multiple reflections from the walls, ceiling or floor.