Interference and beats

Objectives Investigate and analyze characteristics of waves, including frequency and amplitude. Investigate and analyze behaviors of waves, including constructive and destructive interference. Describe the role of wave interference in industrial applications such as noise cancellation technology.

Assessment What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase? Noise-canceling headphones use destructive interference. Which of the following explains destructive interference? harmonic motion refraction Fourier's theorem superposition principle

Physics terms echo reverberation phase beats active noise cancellation

Echoes and reverberation An echo is a reflected sound wave. If you clap your hands 170 meters away from a large wall . . .

Echoes and reverberation An echo is a reflected sound wave. If you clap your hands 170 meters away from a large wall . . . the sound will echo back to you one second later. What happens if you clap or sing in a shower stall, where the wall is much closer? What do you hear?

Echoes and reverberation In an auditorium you hear music directly from the stage AND a multiple echo called reverberation. Sound from this performer travels to the listener via three paths. Which path is the direct path? Which paths are the echoes? Do they all arrive at the same time? A B C

Echoes and reverberation In an auditorium you hear music directly from the stage AND a multiple echo called reverberation. Sound from this performer travels to the listener via three paths. Which path is the direct path? B Which paths are the echoes? A, C Do they all arrive at the same time? A B C A and C are almost simultaneous with B.

Echoes and reverberation Reverberation is the addition of multiple reflections of a sound to the original sound. This adds liveliness, depth, and richness to sound. Reverberation is why it’s so fun to sing in the shower.

Echoes and reverberation Acoustical engineers design concert halls to create the right amount of “reverb”. There should be no “dead” spots where sound waves interfere destructively.

Echoes and reverberation Absorbent wall panels dampen side reflections Acoustical engineers design concert halls to create the right amount of “reverb”. There should be no “dead” spots where sound waves interfere destructively. Some auditoriums have panels that can be rearranged to balance the reverberation for different performances. Angled back walls help project sound forward if time allows, a class might take a mini field trip to their school auditorium to examine at the acoustic features.

Phase A full wave has a phase of 360 degrees. Interference between two or more sound waves depends on their phase difference.

Constructive interference Two waves are in phase when both begin at the same point in their cycle. Waves that are in phase interfere constructively.

Destructive interference Two waves are out of phase if one wave begins half a cycle ahead or behind the other. Waves that are out of phase interfere destructively.

Two frequencies What happens when two simultaneous sound waves are very close in frequency? To find out, click the simulation on page 458.

Engaging with the concepts Create a set of two sound waves at 440 Hz and 441 Hz. Set time to 5 s. Can you see the beats? Can you hear the beats? What is the beat frequency?

Engaging with the concepts Change the frequencies to 440 Hz and 442 Hz. How does the beat frequency change? Does it increase or decrease?

Engaging with the concepts What is the formula for the beat frequency? Test your hypothesis with a new set of frequencies. You may need to adjust the time scale to see the beats. What wave behavior causes beats?

Beats When two frequencies are close but not the same, the sound waves drift in and out of phase, making beats. When the waves are in phase, they add to create a louder wave. When the waves are out of phase they cancel, reducing the sound. The result is a “beat envelope” with its own beat frequency.

Test your knowledge What is the beat frequency between a 120 Hz wave and a 140 Hz wave?

Test your knowledge What is the beat frequency between a 120 Hz wave and a 140 Hz wave? 20 Hz (20 beats per second).

Beats and tuning Musicians listen for beats when tuning their instruments. When the beats disappear, the instruments are in tune with each other. This last set of slides provides examples of useful applications of sound wave interference.

Applications of interference Tuning an instrument by using beats is one application of interference. Can you think of any other applications? Why might you want to use destructive interference?

Noise reduction There are sounds you WANT to hear and sounds you DON’T want to hear. Sound wave interference can be used to help get rid of unwanted sound.

Noise reduction Typical background noise has: Sound you WANT to hear generally has: amplitude that is relatively constant typically low frequency amplitude that changes quickly frequency above a few hundred hertz.

Active noise cancellation A microphone in these noise-canceling headphones samples the external noise. The microphone is connected to a computer chip that controls a miniature amplifier. The amplifier drives a speaker inside the head phones that sends canceling sound waves directly into your ear.

Noise + anti-noise = quiet

Assessment What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase?

Assessment What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase? Two waves that are 180° apart in their cycles will be out of phase, because they will be one half wavelength apart. These waves will interfere destructively. If the waves have the same amplitude, they will cancel each other out completely. This is the idea behind noise-canceling headphones.

Assessment Noise-canceling headphones use destructive interference. Which of the following explains destructive interference? harmonic motion refraction Fourier's theorem superposition principle

Assessment Noise-canceling headphones use destructive interference. Which of the following explains destructive interference? harmonic motion refraction Fourier's theorem superposition principle