Presentation is loading. Please wait.

Presentation is loading. Please wait.

Interference of Sound Waves

Similar presentations

Presentation on theme: "Interference of Sound Waves"— Presentation transcript:

1 Interference of Sound Waves

2 Interference 2 waves, of the same frequency; out of phase.
Eg. y1=A0sin (kx - wt) y2=A0sin (kx - wt +f) Then yR=ARsin(kx-wt+f /2), and the resultant amplitude is AR=2A0cos(½f ). Identical waves which travel different distances will arrive out of phase and will interfere, so that the resultant amplitude varies with location.

3 Quiz You are located at position y, where you can hear a loud
sound - the first maximum in intensity from two speakers. The speakers are then connected ‘out of phase’ (difference of π). What will you hear? A) no change – same loud sound B) no sound C) something between ‘no sound’ and ‘loud sound’ y

4 Example: Two sources, in phase; waves arrive at P by paths of different lengths: S1 P x1 detector x2 At P: S2

5 Phase difference : = Define x to be the path difference Then (using trig), at detector: kx terms don’t cancel!

6 Example A pair of speakers is separated by 3.0m and driven by the
same oscillator. The listener walks perpendicular from a point on the centerline 8m away to a distance of 0.35m before reaching the first minimum in sound intenstiy. What is the frequency of the oscillator? 8.0m 0.35m 3m

7 Solution

8 Intensity I I = Power per unit area Units: W / m2
(the area is measured perpendicular to the wave velocity) Intensity is proportional to (resultant amplitude)2 , since I=P/A and power is proportional to A2 Two sources, each with amplitude Ao, intensity Io , phase difference f:

9 Notes: Maximum IR is 4 x IO Maxima when f = 0, 2π, 4π, 6π , … Minima (zero intensity) when f = π, 3π, 5π , … x = 0, ± λ, ± 2λ,…  x = ± λ/2, ± 3λ/2, ± 5λ/2,… Note: The sources are in phase !!!

10 I think I hear something!
Example 6 m x The detector I think I hear something! 2 speakers, same intensity, in phase; f = 170 Hz (so l = 2.0 m when speed of sound is 340 m/s) At the position x=9 m, find the intensity in terms of the intensity of a single speaker

11 Solution

Download ppt "Interference of Sound Waves"

Similar presentations

Ads by Google