FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS
FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS
11th Edition
ISBN: 9781119459132
Author: Halliday
Publisher: WILEY
Question
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Chapter 17, Problem 1Q
To determine

To find:

a) The rank of phase difference according to the average rate of transport of energy by the waves, greatest first.

b) The average rate of energy transport for the first choice in (a).

Expert Solution & Answer
Check Mark

Answer to Problem 1Q

Solution:

a) The rank of phase difference according to the average rate of transport of energy by the waves, greatest first, is  ϕ=0 , ϕ=0.2 λ and ϕ=0.5 λ

b) The average rate of energy transport for (a) Pavg=4Pavg1

Explanation of Solution

1) Concept:

The rate of energy transported by a travelling wave depends on the intensity of the wave as well as the area to which the energy is transported. The intensity of a resultant wave depends on the phase difference between the two superposing waves.

2) Formula:

P= I.A

3) Given:

i) The average rate of energy transported by a single wave = Pavg1

ii)  The phase difference between the two waves sent through the pipe are  ϕ=0 , ϕ=0.2 λ  and ϕ=0.5 λ

4) Calculations:

a) The rate of energy transported is given by

P= I.A

I is intensity of the wave and A is area to which the energy is transported.

When two waves are sent with phase difference  ϕ1=0 ; the two waves will coincide exactly with each other. There will be constructive interference between the two and the resultant amplitude will be twice the original amplitude. Hence, the intensity of the resultant wave will be 4 times the original. (Since  I=A2)

Thus, the rate of energy transport for ϕ1=0 will be more than that for a single wave.

When two waves are sent with phase difference  ϕ2=0.2 λ ; the two waves will coincide partially. There will be partial constructive interference between the two waves.

Hence, the resultant intensity will be more than the single wave but less than that for ϕ1=0

When two waves are sent with phase difference  ϕ3=0.5 λ ; the two waves will show destructive interference. i.e the resultant wave will be a standing wave and not a travelling wave. Hence, it will not transport the energy.

Hence, the ranking of the situations will be

Pφ=0>Pφ=0.2λ>Pφ=0.5 λ

b) Since the amplitude of the resultant wave is twice the single wave, intensity is four fold. Hence, the rate of energy transported will be

Pavg=I .A

Pavg= 4I1.A

 Pavg=4 . Pavg 1

Conclusion:

The energy transported by a wave can be calculated by using the intensity of the wave. Here, the intensity changes according to the phase difference between the two superposing waves. Hence the rate of energy transported changes as the phase difference changes.

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Chapter 17 Solutions

FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS

Ch. 17 - You are given four tuning forks. The fork with the...Ch. 17 - Two spectators at a soccer game see, and a moment...Ch. 17 - What is the bulk modulus of oxygen if 32.0 g of...Ch. 17 - Prob. 3PCh. 17 - A column of soldiers, marching at 120 paces per...Ch. 17 - Prob. 5PCh. 17 - A man strikes one end of a thin rod with a hammer....Ch. 17 - SSM WWW A stone is dropped into a well. The splash...Ch. 17 - Prob. 8PCh. 17 - If the form of a sound wave traveling through air...Ch. 17 - Prob. 10PCh. 17 - SSM Diagnostic ultrasound of frequency 4.50 MHz is...Ch. 17 - The pressure in a traveling sound wave is given by...Ch. 17 - A sound wave of the form s = sm coskx t travels...Ch. 17 - Figure 17-32 shows the output from a pressure...Ch. 17 - GO A handclap on stage in an amphitheater sends...Ch. 17 - Two sound waves, from two different sources with...Ch. 17 - Prob. 17PCh. 17 - Prob. 18PCh. 17 - GO Figure 17-35 shows two isotropic point sources...Ch. 17 - Figure 17-36 shows four isotropic point sources of...Ch. 17 - SSM In Fig. 17-37, two speakers separated by...Ch. 17 - In Fig. 17-38, sound with a 40.0 cm wavelength...Ch. 17 - GO Figure 17-39 shows two point sources S1 and S2...Ch. 17 - Suppose that the sound level of a conversation is...Ch. 17 - A sound wave of frequency 300Hz has an intensity...Ch. 17 - Prob. 26PCh. 17 - SSM WWW A certain sound source is increased in...Ch. 17 - Two sounds differ in sound level by 1.00 dB. 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Find...Ch. 17 - Prob. 73PCh. 17 - The average density of Earths crust 10 km beneath...Ch. 17 - A certain loudspeaker system emits sound...Ch. 17 - Find the ratios greater to smaller of the a...Ch. 17 - Prob. 77PCh. 17 - A trumpet player on a moving railroad flatcar...Ch. 17 - GO In Fig. 17-46, sound of wavelength 0.850 m is...Ch. 17 - GO A detector initially moves at constant velocity...Ch. 17 - SSMa If two sound waves, one in air and one in...Ch. 17 - A continuous sinusoidal longitudinal wave is sent...Ch. 17 - SSMUltrasound, which consists of sound waves with...Ch. 17 - The speed of sound in a certain metal is vm. One...Ch. 17 - An avalanche of sand along some rare desert sand...Ch. 17 - A sound source moves along an x axis, between...Ch. 17 - SSMA siren emitting a sound of frequency 1000 Hz...Ch. 17 - Prob. 88PCh. 17 - Prob. 89PCh. 17 - Prob. 90PCh. 17 - Prob. 91PCh. 17 - You can estimate your distance from a lightning...Ch. 17 - SSMFigure 17-48 shows an air-filled, acoustic...Ch. 17 - Prob. 94PCh. 17 - SSMThe sound intensity is 0.0080 W/m2 at a...Ch. 17 - Four sound waves are to be sent through the same...Ch. 17 - Prob. 97PCh. 17 - A point source that is stationary on an x axis...Ch. 17 - You are standing at a distance D from an isotropic...Ch. 17 - Pipe A has only one open end; pipe B is four times...Ch. 17 - A pipe 0.60 m long and closed at one end is filled...Ch. 17 - A sound wave travels out uniformly in all...Ch. 17 - A police car is chasing a speeding Porsche 911....Ch. 17 - Prob. 104PCh. 17 - In Fig. 17-35. S1 and S2 are two isotropic point...Ch. 17 - Prob. 106PCh. 17 - Kundts method for measuring the speed of sound. In...Ch. 17 - Prob. 108PCh. 17 - In Fig. 17-53, a point source S of sound waves...Ch. 17 - A person on a railroad car blows a trumpet note at...Ch. 17 - A listener at rest with respect to the air and the...
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