Question

A row of seats is parallel to a stage at a distance of 90 m from it. At the center and front of the stage is a diffraction horn loudspeaker. This speaker sends out its sound through an opening that is like a small doorway with a width D of 0.070 m. The speaker is playing a tone that has a frequency of 4.00 x 10 Hz. The speed of sound is 343 m/s. What is the separation between two seats, located near the center of the row, at which the tone cannot be heard?

Answer 1

Answer:

distance between seats = 2*11.10 = 22.20 m

Explanation:

seats row is parallel to a stage with a distance d = 90 m

doorway width = 0.070 m

speaker frequency = 4.00 * 10^4 Hz

Speed of sound = 343 m/s

tone will be heard at

$sin \theta = \frac{\lambda}{D}$

we know that $v =\lambda d$

so

$sin\theta = \frac{v}{dD}$

              $= \frac{343}{4.00 * 10^4*0.070}$

$sin\theta = 0.1225$

$\theta = 7.036 degree$

$tan\theta =\frac{x}{d}$

[tex]x = d*tan\theta = 90*0.1234 = 11.10 m

distance between seats = 2*11.10 = 22.20 m