Answer:
Width of sound beam is 7.557 m
Explanation:
First we will calculate the wave length from given data:
λ=v/f
Were:
v is the speed
f is the frequency
[tex]\lambda=\frac{340}{30*10^3}\\ \lambda=0.01133 m[/tex]
We considered the opening long and narrow, Using single slit diffraction formula:
mλ=dsinΘ
where:
d is the crack width
m is the order
Θ is angle
Considering m=1, The angle between first minimum from center of beam is:
[tex]\theta=sin^{-1}(\frac{m\lambda}{d})\\\theta=sin^{-1}(\frac{1*0.01133}{30*10^{-2}})\\ \theta=2.164^o[/tex]
The width of beam is:
tanΘ=y/L
[tex]tan\theta=\frac{w/2}{L}\\ w=2L\ tan\theta\\w=2*100*tan 2.164\\w=7.557 m[/tex]
Width=7.557 m
