Answer
(a) The beat frequency is $9~Hz$
(b) The distance between regions of maximum intensity is 38.1 meters.
Work Step by Step
(a) We can find $f_1$ as:
$f_1 = \frac{v}{\lambda_1}$
$f_1 = \frac{343~m/s}{2.54~m}$
$f_1 = 135~Hz$
We can find $f_2$ as:
$f_2 = \frac{v}{\lambda_2}$
$f_2 = \frac{343~m/s}{2.72~m}$
$f_2 = 126~Hz$
Since the beat frequency is the difference between the two frequencies, the beat frequency is $9~Hz$.
(b) We can find the distance between regions of maximum intensity as:
$\lambda = \frac{v}{f}$
$\lambda = \frac{343~m/s}{9~Hz}$
$\lambda = 38.1~m$
The distance between regions of maximum intensity is 38.1 meters.
