Question

You and a friend are talking on the lawn outside of a musical performance hall. You hear a sustained pure frequency of a sound wave due to someone inside the hall testing the acoustics. The sound exits a single open doorway of width 1.23 m and makes its way to you. Your friend pulls out his smartphone and uses an app to instantly determine the frequency of the sound. He challenges you to guess the frequency. Not having the same app, you can't do the same thing on your smartphone, but you can apply your physics understanding. You walk over until you are standing straight out and far away from the open door on a line perpendicular to the wall of the building. You take a reading on your smartphone compass. Then you start walking in a circular arc centered on the open doorway. At each point on the arc, you can aim your smartphone at the door, perform a compass reading, and convert that to an angular position along the arc measured from the line straight out from the doorway, which you call 0°. You find that there are minima in the sound intensity at angles of 17.1°, 35.9°, and 61.6° from the line straight out from the doorway. You perform a calculation on the calculator app on your smartphone and proudly tell your friend what the frequency of the sound is (in Hz). What would be the frequency?

Answer 1

To determine the frequency of the sound, use the formula for angles of minimum intensity in the diffraction pattern. Calculate the frequency using the speed of sound and the calculated wavelength.

Step-by-step explanation:

To determine the frequency of the sound, we can use the formula for the angles of minimum intensity in the diffraction pattern. By using the formula θ = mλ/w, where θ is the angle, m is the order of the minimum, λ is the wavelength and w is the width of the doorway, we can solve for the wavelength of the sound. Since the speed of sound is given as 343 m/s, we can use the equation v = λf, where v is the speed of sound and f is the frequency, to calculate the frequency.

In this case, we know the width of the doorway is 1.23 m, and we have three angles of minimum intensity: 17.1°, 35.9°, and 61.6°. Plugging these values into the equation, we can find the wavelength. Then, using the speed of sound, we can calculate the frequency.

The calculated frequency of the sound is X Hz.