Concept explainers
The relative minima of sound pressure located on the joining the two speakers.
Answer to Problem 70PQ
The relative minima of sound pressure located on the joining the two speakers are
Explanation of Solution
Write an expression for the space between the nodes.
Here,
Write an expression for the wavelength.
Here,
Substitute equation (II) in figure (I).
For speakers vibrating in phase, the antinode of the pressure is the point halfway between the speakers.
Write the expression for the distance of antinode of pressure from each speaker.
Here,
There is a node one quarter of a wavelength away.
Write an expression for the distance of the node.
Here,
After the node, there is a node one quarter of a wavelength.
Write an expression for the nodes.
Here,
Figure 1 shows the position of minimum between the speaker.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the relative minima of sound pressure located on the joining the two speakers are
Want to see more full solutions like this?
Chapter 18 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- Two identical loudspeakers 10.0 m apart are driven by the same oscillator with a frequency of f = 21.5 Hz (Fig. P17.6) in an area where the speed of sound is 344 m/s. (a) Show that a receiver at point A records a minimum in sound intensity from the two speakers. (b) If the receiver is moved in the plane of the speakers, show that the path it should take so that the intensity remains at a minimum is along the hyperbola 9x2 16y2 = 144 (shown in red-brown in Fig. P17.6). (c) Can the receiver remain at a minimum and move very far away from the two sources? If so, determine the limiting form of the path it must take. If not, explain how far it can go. Figure P17.6arrow_forwardA sound wave in air has a pressure amplitude equal to 4.00 103 Pa. Calculate the displacement amplitude of the wave at a frequency of 10.0 kHz.arrow_forwardA pipe is observed to have a fundamental frequency of 345 Hz. Assume the pipe is filled with air (v = 343 m/s). What is the length of the pipe if the pipe is a. closed at one end and b. open at both ends?arrow_forward
- As you travel down the highway in your car, an ambulance approaches you from the rear at a high speed (Fig. OQ17.3) sounding its siren at a frequency of 500 Hz. Which statement is correct? (a) You hear a frequency less than 500 Hz. (b) You hear a frequency equal to 500 Hz. (c) You hear a frequency greater than 500 Hz. (d) You hear a frequency greater than 500 Hz. whereas the ambulance driver hears a frequency lower than 500 Hz. (e) You hear a frequency less than 500 Hz. whereas (he ambulance driver hears a frequency of 500 Hz.arrow_forwardIn Figure OQ14.3, a sound wave of wavelength 0.8 m divides into two equal parts that recombine to interfere constructively, with the original difference between their path lengths being |r2 − r1| = 0.8 m. Rank the following situations according to the intensity of sound at the receiver from the highest to the lowest. Assume the tube walls absorb no sound energy. Give equal ranks to situations in which the intensity is equal. (a) From its original position, the sliding section is moved out by 0.1 m. (b) Next it slides out an additional 0.1 m. (c) It slides out still another 0.1 m. (d) It slides out 0.1 m more. Figure OQ14.3arrow_forwardA piano tuner uses a 512-Hz tuning fork to tune a piano. He strikes the fork and hits a key on the piano and hears a beat frequency of 5 Hz. He tightens the string of the piano, and repeats the procedure. Once again he hears a beat frequency of 5 Hz. What happened?arrow_forward
- Two speakers, facing each other and separated by a distance d, each emit a pure tone of the same amplitude A with frequency f. The speed of each of the sound waves is vs. A listener stands between the speakers, a distance x from one of the speakers. a. What frequencies would cause a dead spot (complete destructive interference) at the listeners position? b. If the speakers are separated by 5.00 m with the listener 2.00 m from one of the speakers, what is the lowest frequency for which there is a dead spot? The speed of sound in air is 343 m/s.arrow_forwardTwo identical loudspeakers 2.0 m apart are emitting 1800 Hz sound waves into a room where the speed of sound is 340 m/s. Is the point 4.0 m directlyin front of one of the speakers, perpendicular to the line joining the speakers, a point of maximum constructive interference, perfect destructive interference, or something in between?arrow_forwardTwo small speakers are driven by a common oscillator at 7.40 × 102 Hz. The speakers face each other and are separated by d = 1.22 m. Locate all points along a line joining the two speakers where relative minima would be expected.arrow_forward
- A speaker is producing spherically symmetric sounds with a total power of 88.5 W. If the speaker is located at the centre of a sphere with a radius of 2.20 m, what is the power received on a 1.70 m by 1.50 m area on the sphere? Give your answer in Watts to 2 decimal places.arrow_forwardTwo identical loudspeakers 2.0 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 5.0 m in front of one of the speakers, perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound. What is the lowest possible frequency of sound for which this is possible?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University