Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 17 - Waves-II - Problems - Page 507: 21a

Answer

$f_{min,1} = 343~Hz$

Work Step by Step

We can find the distance from the upper speaker to the listener: $d = \sqrt{(2.00~m)^2+(3.75~m)^2} = 4.25~m$ We can find the path length difference: $\Delta L = 4.25~m-3.75~m = 0.50~m$ To produce fully destructive interference, $\frac{\Delta L}{\lambda} = 0.5, 1.5, 2.5,...$ Then: $\lambda = \frac{\Delta L}{0.5}, \frac{\Delta L}{1.5},\frac{\Delta L}{2.5},...$ We can find the lowest frequency that produces fully destructive interference: $f_{min,1} = \frac{v}{\lambda}$ $f_{min,1} = \frac{v}{\Delta L/0.5}$ $f_{min,1} = \frac{0.5~v}{\Delta L}$ $f_{min,1} = \frac{(0.5)~(343.~m/s)}{0.50~m}$ $f_{min,1} = 343~Hz$
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