• Constructive Interference – Result is a larger amplitude

When Two Waves Meet…

Destructive Interference – Result is a smaller amplitude

Waves pass through each other afterwards.

If two waves combine...

• Constructive Interference– Waves must be a whole-number wavelength apart

Interference by Position

Destructive Interference– Waves must be a half wavelength apart

If you have the same sound but from two different speakers…

• Path difference of ½ λ leads to destructive interference

Interference by Position

Destructive

Constructive

• A real problem for acoustical engineers

Dead Zones in Concert Halls

Ex. Avery Fisher Concert Hall – Lincoln Center

Newly designed concert hall, Minneapolis, MN

• Two speakers are 1.00 m apart. A person stands 4.00 m away from one of the speakers. How far must this person be from the second speaker in order to detect destructive interference when the speakers emit a 1150 Hz sound in room temperature air.

Example 7

• If two sounds are only slightly off in terms of frequency

The ‘Beats’

Produce a periodic rise and fall of amplitude (volume)

Throbbing Sound = Beats

• #‘beats’ = how far apart the two frequencies are

The ‘Beats’

Ex. Tuning Fork 1: f = 440 HzTuning Fork 2: f = *Beat Frequency of 2 Hz?

• A guitar string produces 4 beats per second when tuned with a 350 Hz tuning fork and 9 beats per second when tuned with a 355 Hz tuning fork. What is the actual frequency of the guitar?

Example 8

• What about the rubber bands determines pitch?

Musical Instruments - Strings

The pitch or frequency of a string is determined by the string’s velocity (how fast it can move back and forth)

FT = Force of Tension

m/L = (mass)/(Length) = Linear Density

Tension Thickness