To determine To find : The time that has elapsed between two measurements of sound intensity produced by the rocket. Explanation Given data: The rocket starts from rest, and travels straight up with an acceleration of 58.0 m s 2 . The rocket produces a sound when it is at the height of 562 m, and the sound eventually reaches the ground-based monitoring station. The sound is emitted uniformly in all the directions. The intensity measured by the monitoring station is I . Later, the station measures an intensity of 1 3 I . There are no reflections of sound in the given system. Speed of the sound ( v s ) is 343 m s . Formula used: As the rocket emitted the sound uniformly in all the directions, the energy carried by the sound wave spreads out uniformly over concentric sphere increasing radii r 1 , r 2 , and so on. Consider the radius of the sphere as r 1 , when the sound intensity measured at the ground is I (position of 1 of the rocket). Consider the radius of the sphere as r 2 , when the sound intensity measured at the ground is 1 3 I (position of 2 of the rocket). Consider the time required for the energy to spread out over the sphere of radius r 1 as t 1 . Write the expression for time required for the energy to spread out over the sphere of radius r 1 as follows. t 1 = r 1 v s (1) Here, v s is the speed of the sound. Consider the time required for the energy to spread out over the sphere of radius r 2 as t 2 . Write the expression for time required for the energy to spread out over the sphere of radius r 2 as follows. t 2 = r 2 v s (2) As the sound wave emitted at position 1 spreads out uniformly, the rocket continue to accelerate upward to position 2 with acceleration a y for a time t 12 . Therefore, write the expression for the time that has elapsed between two measurements of sound intensity as follows. t = t 2 − t 1 + t 12 (3) Refer to the equation (3.3b) in the textbook, and modify the expression to find the time t 12 as follows. v 2 = v 1 + a y t 12 (4) Here, v 1 is the speed of the rocket at position 1, v 2 is the speed of the rocket at position 2, and a y is the acceleration of the rocket, which is given as 58.0 m s 2 . Refer to the equation (16.9) in the textbook, and write the expression for sound intensity at a distance of r from the source as follows. I = P 4 π r 2 (5) Here, P is the sound power from the source, and r is the distance from the source of sound. Modify the expression in equation (5) for the intensity measured by the station at the distance of r 1 as follows. I 1 = P 4 π ( r 1 ) 2 (6) Here, r 1 is the radius of the sphere at the position 1 of the rocket, which is given as 562 m, P is the power emitted by the sound, which is equal at all positions of the rocket. Modify the expression in equation (5) for the intensity measured by the station at the distance of r 2 as follows. I 2 = P 4 π ( r 2 ) 2 (7) Here, r 2 is the radius of the sphere at the position 2 of the rocket. From the given data, relation between intensity measured by the station at the position 1 and position 2 as follows. I 2 = 1 3 I 1 Rearrange the expression as follows. I 1 = 3 I 2 From equation (6), and (7), substitute P 4 π ( r 1 ) 2 for I 1 , and P 4 π ( r 2 ) 2 for I 2 , P 4 π ( r 1 ) 2 = 3 [ P 4 π ( r 2 ) 2 ] Simplify the expression as follows. ( r 2 ) 2 = 3 ( r 1 ) 2 r 2 = ( 3 ) r 1 Substitute 562 m for r 1 , r 2 = ( 3 ) ( 562 m ) = 973.4125 m ≃ 973 m Substitute 562 m for r 1 , and 343 m s for v s in equation (1), t 1 = 562 m 343 m s = 1.6384 s ≃ 1.64 s Substitute 973 m for r 2 , and 343 m s for v s in equation (2), t 2 = 973 m 343 m s = 2

10th Edition

ISBN: 9781119081739

Author: CUTNELL

Publisher: WILEY

See similar textbooks

Concept explainers

Shock Waves

Shock waves are common in continuum mechanics, and their dominance is attributable to the fact that they are stronger (or even less) compressible. Substantial perturbations propagated as sudden dynamic changes of a compressible medium supersonically. Sho…

Videos

Question

Chapter 16, Problem 62P

To determine

To find: The time that has elapsed between two measurements of sound intensity produced by the rocket.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 61P

Chapter 16, Problem 63P

Students have asked these similar questions

Can someone help me

3. Four identical small masses are connected in a flat perfect square. Rank the relative rotational inertias (IA, IB, IC) about the three axes of rotation shown. Axes A and B are in the plane of the square, and axis C is perpendicular to the plane, through mass m1. ΙΑ IB m2 m1 m3 Ic m4 (a) IA

Consider the circuit shown in the figure below. (Assume L = 5.20 m and R2 = 440 Ω.) (a) When the switch is in position a, for what value of R1 will the circuit have a time constant of 15.4 µs? (b) What is the current in the inductor at the instant the switch is thrown to position b?

Chapter 16 Solutions

EP PHYSICS (W/ANSWERS+INDEX)

Ch. 16.1 - Prob. 2CYU Ch. 16.2 - 3. A sound wave (a periodic longitudinal wave)...Ch. 16.3 - Prob. 4CYU Ch. 16.3 - Prob. 5CYU Ch. 16.3 - Prob. 6CYU Ch. 16.3 - Prob. 7CYU Ch. 16.3 - Prob. 8CYU Ch. 16.3 - Prob. 9CYU Ch. 16.5 - 10. In a traveling sound wave, are there any...Ch. 16.6 - 11. Do you expect an echo to return to you more...

Ch. 16.6 - 12. Carbon monoxide (CO), hydrogen (H2). and...Ch. 16.6 - Prob. 13CYU Ch. 16.7 - 14. Sonic animals rely on an acute sense of...Ch. 16.7 - Prob. 15CYU Ch. 16.8 - Prob. 16CYU Ch. 16.8 - Prob. 17CYU Ch. 16.9 - Prob. 18CYU Ch. 16.9 - 19. When a car is at rest, its horn emits a...Ch. 16.9 - Prob. 20CYU Ch. 16.9 - Prob. 21CYU Ch. 16.9 - Prob. 22CYU Ch. 16 - Prob. 2FC Ch. 16 - Prob. 3FC Ch. 16 - Prob. 6FC Ch. 16 - Prob. 7FC Ch. 16 - Prob. 10FC Ch. 16 - 11. As the amplitude of a sound wave in air...Ch. 16 - Prob. 12FC Ch. 16 - Prob. 13FC Ch. 16 - Prob. 15FC Ch. 16 - Prob. 17FC Ch. 16 - Prob. 18FC Ch. 16 - Prob. 19FC Ch. 16 - Prob. 1P Ch. 16 - Prob. 2P Ch. 16 - Prob. 3P Ch. 16 - Prob. 4P Ch. 16 - Prob. 5P Ch. 16 - Prob. 6P Ch. 16 - Prob. 7P Ch. 16 - Prob. 8P Ch. 16 - Prob. 9P Ch. 16 - Prob. 10P Ch. 16 - Prob. 11P Ch. 16 - Prob. 12P Ch. 16 - Prob. 13P Ch. 16 - Prob. 14P Ch. 16 - Prob. 15P Ch. 16 - Prob. 16P Ch. 16 - Prob. 17P Ch. 16 - Prob. 18P Ch. 16 - Prob. 19P Ch. 16 - Prob. 20P Ch. 16 - Prob. 21P Ch. 16 - Prob. 22P Ch. 16 - Prob. 23P Ch. 16 - Prob. 24P Ch. 16 - Prob. 25P Ch. 16 - Prob. 26P Ch. 16 - Prob. 27P Ch. 16 - Prob. 28P Ch. 16 - Prob. 29P Ch. 16 - Prob. 30P Ch. 16 - Prob. 31P Ch. 16 - Prob. 32P Ch. 16 - Prob. 33P Ch. 16 - Prob. 34P Ch. 16 - Prob. 35P Ch. 16 - Prob. 36P Ch. 16 - Prob. 37P Ch. 16 - Prob. 38P Ch. 16 - Prob. 39P Ch. 16 - Prob. 40P Ch. 16 - 41. An explosion occurs at the end of a pier. The...Ch. 16 - Prob. 42P Ch. 16 - Prob. 43P Ch. 16 - Prob. 44P Ch. 16 - Prob. 45P Ch. 16 - Prob. 46P Ch. 16 - Prob. 47P Ch. 16 - Prob. 48P Ch. 16 - Prob. 49P Ch. 16 - Prob. 50P Ch. 16 - Prob. 51P Ch. 16 - Prob. 52P Ch. 16 - Prob. 53P Ch. 16 - 54. A source of sound is located at the center of...Ch. 16 - Prob. 55P Ch. 16 - Prob. 56P Ch. 16 - 57. A loudspeaker has a circular opening with a...Ch. 16 - Prob. 58P Ch. 16 - Prob. 59P Ch. 16 - Prob. 60P Ch. 16 - Prob. 61P Ch. 16 - 62. A rocket, starting from rest, travels straight...Ch. 16 - Prob. 63P Ch. 16 - Prob. 64P Ch. 16 - Prob. 65P Ch. 16 - Prob. 66P Ch. 16 - Prob. 67P Ch. 16 - Prob. 68P Ch. 16 - Prob. 69P Ch. 16 - Prob. 70P Ch. 16 - Prob. 71P Ch. 16 - Prob. 72P Ch. 16 - 73. A portable radio is sitting at the edge of a...Ch. 16 - Prob. 74P Ch. 16 - Prob. 75P Ch. 16 - Prob. 76P Ch. 16 - Prob. 77P Ch. 16 - Prob. 78P Ch. 16 - Prob. 79P Ch. 16 - Prob. 80P Ch. 16 - 81. a car is parked 20.0 m directly south of a...Ch. 16 - 82. A loudspeaker in a parked car is producing...Ch. 16 - Prob. 83P Ch. 16 - Prob. 84P Ch. 16 - Prob. 85P Ch. 16 - Prob. 86P Ch. 16 - Prob. 87P Ch. 16 - Prob. 88P Ch. 16 - 89. A recording engineer works in a soundproofed...Ch. 16 - Prob. 90AP Ch. 16 - Prob. 91AP Ch. 16 - Prob. 92AP Ch. 16 - Prob. 93AP Ch. 16 - Prob. 94AP Ch. 16 - Prob. 95AP Ch. 16 - Prob. 96AP Ch. 16 - Prob. 97AP Ch. 16 - Prob. 98AP Ch. 16 - Prob. 99AP Ch. 16 - Prob. 100AP Ch. 16 - Prob. 101AP Ch. 16 - Prob. 102AP Ch. 16 - Prob. 103AP Ch. 16 - Prob. 104AP Ch. 16 - Prob. 105AP Ch. 16 - 106. spider hangs from a strand of silk whose...Ch. 16 - Prob. 107AP Ch. 16 - Prob. 108AP Ch. 16 - Prob. 109AP Ch. 16 - Prob. 110AP Ch. 16 - Prob. 111AP Ch. 16 - Prob. 112CCP Ch. 16 - Prob. 113CCP

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.