18. Waves & Sound

Two sinusoidal waves with amplitudes $4.5\mathrm{cm}$ and $3.0\mathrm{cm},$ 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?

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?

You are standing $3.0\mathrm{m}$ from one speaker and $2.5\mathrm{m}$ from another. Both are emitting identical 680 Hz tones in phase. What best describes what you would observe? Use $340\text{ m/s}$ for the speed of sound.

Two speakers (A and B) lie on the y-axis, $4.0\mathrm{m}$ 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 $340\text{ m/s}.$

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)

. (a) At what distance d will the sound from the speakers first produce destructive interference at the listener's location?

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

Fig. E16.39. For what frequencies does their sound at the speakers produce (a) constructive interference

Two loudspeakers, A and B (Fig. E16.35)

, 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?

Two loudspeakers, A and B (Fig. E16.35)

, 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

What are the sound intensity levels for sound waves of intensity (a) 3.0 x 10⁻⁶ W/m²?

A sound source is located somewhere along the x-axis. Experiments show that the same wave front simultaneously reaches listeners at x = ─7.0 m and x = ＋3.0 m. a. What is the x-coordinate of the source?

The three identical loudspeakers in FIGURE P17.71 play a 170 Hz tone in a room where the speed of sound is 340 m/s . You are standing 4.0 m in front of the middle speaker. At this point, the amplitude of the wave from each speaker is a.

c. When the amplitude is maximum, by what factor is the sound intensity greater than the sound intensity from a single speaker?

The three identical loudspeakers in FIGURE P17.71 play a 170 Hz tone in a room where the speed of sound is 340 m/s . You are standing 4.0 m in front of the middle speaker. At this point, the amplitude of the wave from each speaker is a. b. How far must speaker 2 be moved to the left to produce a maximum amplitude at the point where you are standing?

FIGURE EX17.27 shows the circular wave fronts emitted by two wave sources. b. Make a table with rows labeled P, Q, and R and columns labeled r1 ,r2 , Δr , and C/D. Fill in the table for points P, Q, and R, giving the distances as multiples of λ and indicating, with a C or a D, whether the interference at that point is constructive or destructive.

Two speakers, emitting identical sound waves of wavelength 2.0 m in phase with each other, and an observer are located as shown in

Fig. E35.5. (a) At the observer's location, what is the path difference for waves from the two speakers?

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?

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 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 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?

Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 34 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks so that he is always 1.50 m from speaker B

(Fig. E35.1). For what values of x will the sound this person hears be (b) cancelled? Limit your solution to the cases where x … 1.50 m

Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 34 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks so that he is always 1.50 m from speaker B

(Fig. E35.1). For what values of x will the sound this person hears be (a) maximally reinforced. Limit your solution to the cases where x … 1.50 m