Loudspeaker Design: Calculating Angle of First Minimum

[_Mayday_]

Hey,

I've just done a bit of reading on some simple loudspeaker design in my textbook. It is asking me to calculate when the first minimum occurs. I think I am fine with this, but my problem is that I have no idea how I would calculate the angle at which the minimum occurs.

I will use an example given in the book. The sound frequency is 0.14 m and this is emitted by a loudspeaker of diametre 0.15 m.

I am using the equation:

$$sin\theeta=\frac{\lambda}{b}$$

I would therefor say that the first minum occurs at $$\frac{0.14}{0.15}=0.93 \degrees$$

The book however says that the angle at which the minimum occurs is about 69 degrees. Could someone please clear this up, it is probably a misunderstanding of some sort. I have not offered working as I do not know the method in solving this, but any help would be great.

Thanks.

_Mayday_

 

[hage567]

The sound frequency is 0.14 m

I'm assuming you meant to say wavelength??

It looks to me like you just didn't finish the calculation. Use your calculator to compute the angle.

 

[_Mayday_]

Yes, sorry I did mean wavelength. What do you mean I didn't complete the calculation? Are you saying that I have the correct equation to give me that answer?

 

[hage567]

You have $$\sin\theta = \frac{0.14}{0.15}$$

Solve for theta and you should get 69.0 degrees.

 

[_Mayday_]

I can't believe I missed that...

Thanks for your time.