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

distance between seats = 2*11.10 = 22.20 m

Step-by-step 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 = (\lambda)/(D)`

we know that
`v =\lambda d`

so

`sin\theta = (v)/(dD)`

`= (343)/(4.00 * 10^4*0.070)`

`sin\theta = 0.1225`

`\theta = 7.036 degree`

`tan\theta =(x)/(d)`

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

distance between seats = 2*11.10 = 22.20 m