18. Waves & Sound

Wave Interference

Wave Superposition Introduction

Wave Interference | Arbor Scientific

Two sinusoidal waves with amplitudes <math display=“inline”><mrow><mn>4</mn><mo>.</mo><mrow><mn>5</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></mrow></math> and <math display=“inline”><mrow><mn>3</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow><mo>,</mo></mrow></math> respectively, move toward each other on a string and experience superposition. As they move past each other, the displacement of the string from equilibrium is complicated. Considering all positions on the string where the waves are overlapping, what are the largest and smallest magnitudes of the displacement of the string?

Waves - Interference Phase Angle

Interference, Reflection, and Diffraction

 The 50 Hz tone seems 40 times louder than the 10,000 Hz tone. 

 The 50 Hz tone seems 1000 times louder than the 10,000 Hz tone. 

 The 10,000 Hz tone seems three times louder than the 50 Hz tone. 

 The 10,000 Hz tone seems 40 times louder than the 50 Hz tone. 

 If the intensities are the same, they will seem to have the same sound intensity level. 

 The 50 Hz tone seems three times louder than the 10,000 Hz tone. 

 Suppose you are listening to two tones, one of 50 Hz, and the other of 10,000 Hz. If the sources of these tones are equal in intensity at your location, which do you perceive to have a higher sound intensity level (in dB), and by what factor? 

The Double-Slit Experiment

Two speakers (A and B) lie on the y-axis, <math display=“inline”><mrow><mn>4</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> apart. They emit exactly the same 280 Hz tone in phase with each other. You start right at speaker A and walk in the x-direction. How far from speaker A do you first hear a minimum in sound intensity? Assume the speed of sound in this room is <math><mrow><mn>340</mn><mtext></mtext><mtext>&#x00A0;m/s</mtext></mrow><mo>.</mo></math>

 A quiet sound, destructive interference 

 A quiet sound, constructive interference 

 A loud sound, constructive interference 

You are standing <math display=“inline”><mrow><mn>3</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> from one speaker and <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>5</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> from another. Both are emitting identical 680 Hz tones in phase. What best describes what you would observe? Use <math><mrow><mn>340</mn><mtext></mtext><mtext>&#x00A0;m/s</mtext></mrow></math> for the speed of sound.

In the following figure, two interfering waves are drawn at some instance in time.&nbsp;a. Indicate the regions on the graph where constructive interference occurs. b.Indicate the regions on the graph where destructive interference occurs.<img src="https://cdn.clutchprep.com/problem_images/76081-991c8778f8934483.png"alt=""/>

Wave Reflection

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