Answer
It is not possible to hear the whistle clearly at 24 and 54 degrees away from the centerline.
Work Step by Step
The sound is diffracted when it passes through the doorway. Find the possible angles for the minima of sound, using equation 24–3b.
$$D sin \theta=m\lambda = \frac{mv}{f}$$
$$\theta = sin^{-1}\frac{mv}{Df}$$
Let m = 1.
$$\theta = sin^{-1}\frac{(1)(340m/s)}{(0.88m)(950 Hz)}=24^{\circ}$$
Let m = 2.
$$\theta = sin^{-1}\frac{(2)(340m/s)}{(0.88m)(950 Hz)}=54^{\circ}$$
For m = 3 or higher, there is no solution because the sine function is always less than 1.
It is not possible to hear the whistle clearly at 24 and 54 degrees away from the centerline.
