18. Waves & Sound

Wave Interference

Hewitt-Drew-it! PHYSICS 86. Wave Interference

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

Two speakers that are 15.0 m apart produce in-phase sound waves of frequency 250.0 Hz in a room where the speed of sound is 340.0 m>s. A woman starts out at the midpoint between the two speakers. The room’s walls and ceiling are covered with absorbers to eliminate reflections, and she listens with only one ear for best precision. (a) What does she hear: constructive or destructive interference? Why?

Small speakers A and B are driven in phase at 725 Hz by the same audio oscillator. Both speakers start out 4.50 m from the listener, but speaker A is slowly moved away (Fig. E16.34)<img src="https://lightcat-files.s3.amazonaws.com/problem_images/25ce09876012e2fa-1672135930513.jpg" alt="" />. (a) At what distance d will the sound from the speakers first produce destructive interference at the listener’s location?

Two speakers, emitting identical sound waves of wavelength 2.0 m in phase with each other, and an observer are located as shown in <img src="https://lightcat-files.s3.amazonaws.com/problem_images/6ec95705e002134e-1674055483604.jpg" alt="" />Fig. E35.5. (a) At the observer’s location, what is the path difference for waves from the two speakers?<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/54af79caea33732b-1678285617938.jpg" style="width: 198px;">

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>

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=""/>

Two small stereo speakers are driven in step by the same variable-frequency oscillator. Their sound is picked up by a microphone arranged as shown in <img src="https://lightcat-files.s3.amazonaws.com/problem_images/4d566e377a3fa1d5-LR%20speaker.png" alt="" /> Fig. E16.39. For what frequencies does their sound at the speakers produce (a) constructive interference<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/f5412074058319d1-1678285450527.jpg" style="width: 300px;">

Two loudspeakers, A and B (Fig. E16.35)<img src="https://lightcat-files.s3.amazonaws.com/problem_images/891f299f6a99e247-home%20P.png" alt="" />, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q. What is the lowest frequency for which (a) constructive interference occurs at point Q<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/9369180674ccdde2-1678285198441.jpg" style="width: 300px;">

Two speakers that are 15.0 m apart produce in-phase sound waves of frequency 250.0 Hz in a room where the speed of sound is 340.0 m>s. A woman starts out at the midpoint between the two speakers. The room’s walls and ceiling are covered with absorbers to eliminate reflections, and she listens with only one ear for best precision. (c) How far from the center must she walk before she first hears the sound maximally enhanced?

Two loudspeakers, A and B (Fig. E16.35)<img src="https://lightcat-files.s3.amazonaws.com/problem_images/24d5d1cf098b1bb7-1672133549397.jpg" alt="" />, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q. What is the lowest frequency for which (b) destructive interference occurs at point Q?<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/1aee337332a13c68-1678285196946.jpg" style="width: 300px;">

Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. (a) What is the longest wavelength for which there will be destructive interference at point Q?

Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. (b) What is the longest wavelength for which there will be constructive interference at point Q?

Wave Reflection

Wave Superposition Introduction

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