The width of the doorway is 83 cm, and the speed of sound is 343 m/s. Find the diffraction angle when the frequency is each of the following.

(a) 4.8 kHz

If theta is the diffraction angle.

Sine(theta)= lambda/slit width

where lambda = wave length

so you need to find the wavelength
(hint make sure it is the same units as the width)
and then substitute into the above.

I've tried this problem several time and got the wrong answer. Please explain where I am going wrong.

Sine (theata) = Lambda/ slit width
Lambda = wave speed/ wave frequency
Lambda = (34300cm/s)/ (4800Hz)
Lambda = 7.1458

therefore
sine (theata) = 7.1458 / 83cm
sine (theata) = 0.08609
theata = 0.0015

SineTheta= .08609, I agree
Theta= 4.94 degrees.

Can you please explain how you arrived at 4.94 degrees?

I put in my calculator .086, then pressed 2nd Sin, thus getting the angle whose sine is .086

Theta= arcSin .086= 4.94 deg