Fundamentals of Physics Extended (10th Edition)

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

Chapter 36 - Diffraction - Problems - Page 1111: 32a

Answer

$6.8^{\circ}$

Work Step by Step

First, we can use the given frequency, $f=25*10^3Hz$, and the speed of sound in water, $v=1450m/s$, to find the wavelength. $\lambda = v / f$ $\lambda = (1450m/s) / (25*10^3Hz)$ $\lambda =0.058m$ Now we can use the given diameter, $d=0.60m$, in equation (36-12), to find the angle to the first minimum, $\theta$. $\sin \theta= 1.22 \frac{\lambda}{d}$ $ \theta=\arcsin( 1.22 \frac{\lambda}{d})$ $ \theta=\arcsin( 1.22 \frac{0.058m}{0.60m})$ $\theta = 6.8^{\circ}$
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