FUNDAMENTALS OF PHYSICS - EXTENDED
FUNDAMENTALS OF PHYSICS - EXTENDED
12th Edition
ISBN: 9781119773511
Author: Halliday
Publisher: WILEY
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Chapter 16, Problem 1Q
To determine

To rank:

The waves according to

a) their wave speed

b) the tension in the string along which they travel

Expert Solution & Answer
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Answer to Problem 1Q

Solution:

a) The waves can be ranked according to their wave speed as v1>v4>v2>v3(greatest first)

b) The waves can be ranked according to their tension in the string along which they travel as τ1>τ4>τ2>τ3(greatest first)

Explanation of Solution

1) Concept:

We can use the concept of the equation of transverse wave and speed of a travelling wave. The wave speed on a stretched string gives the relation between speed and tension in the string.

2) Formulae:

i) y=ym sinkx-ωt

ii)

v=ωk

iii)

v=τμ

3) Given:

The four waves along the strings with the same linear densities are

i) y1=3 mm sinx-3t

ii) y2=6 mm sin2x-t

iii) y3=1 mm sin4x-t

iv) y4=2 mm sinx-2t

4) Calculations:

a) Rank the waves according to their wave speed :

The equation of transverse wave is

y=ym sinkx-ωt(1)

The speed of the travelling wave is

v=ωk

The equation (i),

y1=3 mm sinx-3t

Compare this equation with equation (1), then the speed of the travelling wave is

v1=31

v1=3

The equation (ii) is

y2=6 mm sin2x-t

Compare this equation with equation (1), then the speed of the travelling wave is

v2=12

v2=0.5

The equation (iii) is

y3=1 mm sin4x-t

Compare this equation with equation (1), then the speed of the travelling wave is

v3=14

v3=0.25

The equation (iv) is

y4=2 mm sinx-2t

Compare this equation with equation (1), then the speed of the travelling wave is

v4=21

v4=2

Hence, the rank of the waves according to the wave speed is v1>v4>v2>v3 (greatest fitst).

b) Rank the waves according to tension:

The wave speed on a stretched string is

v=τμ

v ατ

The speed on the stretched string is directly proportional to the tension in the string with the same linear density.

The speed on the stretched string for equation (i) is

v1 ατ1

The speed on the stretched string for equation (ii) is

v2 ατ2

The speed on the stretched string for equation (iii) is

v3 ατ3

The speed on the stretched string for equation (i) is

v4 ατ4

Hence, the rank of the waves according to their tension is τ1>τ4>τ2>τ3 (greatest first).

Conclusion:

We can find the wave speed by using its expression and rank their values. By using the expression of the speed on the stretched string, we can find thetension in each string and rank their values.

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Chapter 16 Solutions

FUNDAMENTALS OF PHYSICS - EXTENDED

Ch. 16 - A transverse sinusoidal wave is moving along a...Ch. 16 - The equation of a transverse wave traveling along...Ch. 16 - Prob. 11PCh. 16 - GO The function yx, t = 15.0 cm cosx 15 t, with x...Ch. 16 - Prob. 13PCh. 16 - The equation of a transverse wave on a string is y...Ch. 16 - Prob. 15PCh. 16 - The speed of a transverse wave on a string is 170...Ch. 16 - The linear density of a string is 1.6 104 kg/m. A...Ch. 16 - Prob. 18PCh. 16 - SSM What is the speed of a transverse wave in a...Ch. 16 - The tension in a wire clamped at both ends is...Ch. 16 - ILW A 100 g wire is held under a tension of 250 N...Ch. 16 - A sinusoidal wave is traveling on a string with...Ch. 16 - A uniform rope of mass m and length L hangs from a...Ch. 16 - A string along which waves can travel is 2.70 m...Ch. 16 - Prob. 27PCh. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Prob. 31PCh. 16 - What phase difference between two identical...Ch. 16 - Prob. 34PCh. 16 - SSM Two sinusoidal waves of the same frequency...Ch. 16 - Four waves are to be sent along the same string,...Ch. 16 - GO These two waves travel along the same string:...Ch. 16 - Two sinusoidal waves of the same frequency are to...Ch. 16 - Two sinusoidal waves of the same period, with...Ch. 16 - Two sinusoidal waves with identical wavelengths...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - SSM WWW What are a the lowest frequency, b the...Ch. 16 - A 125 cm length of string has mass 2.00 g and...Ch. 16 - Prob. 45PCh. 16 - String A is stretched between two clamps separated...Ch. 16 - Prob. 47PCh. 16 - If a transmission line in a cold climate collects...Ch. 16 - Prob. 51PCh. 16 - A rope, under a tension of 200 N and fixed at both...Ch. 16 - Prob. 53PCh. 16 - GO The following two waves are sent in opposite...Ch. 16 - A standing wave pattern on a string is described...Ch. 16 - A generator at one end of a very long string...Ch. 16 - Prob. 61PCh. 16 - Prob. 62PCh. 16 - A wave has a speed of 240 m/s and a wavelength of...Ch. 16 - The equation of a transverse wave traveling alone...Ch. 16 - The equation of a transverse wave traveling along...Ch. 16 - Prob. 67PCh. 16 - Prob. 69PCh. 16 - A transverse sinusoidal wave is generated at one...Ch. 16 - Prob. 73PCh. 16 - Prob. 74PCh. 16 - a What is the fastest transverse wave that can be...Ch. 16 - A standing wave results from the sum of two...Ch. 16 - Prob. 77PCh. 16 - Prob. 78PCh. 16 - Prob. 79PCh. 16 - When played in a certain manner, the lowest...Ch. 16 - A sinusoidal transverse wave traveling in the...Ch. 16 - Two sinusoidal waves of the same wavelength travel...Ch. 16 - Prob. 83PCh. 16 - Prob. 84PCh. 16 - Prob. 85PCh. 16 - a Write an equation describing a sinusoidal...Ch. 16 - A wave on a string is described by yx, t = 15.0...Ch. 16 - Two waves are described by...Ch. 16 - SSM In a demonstration, a 1.2 kg horizontal rope...Ch. 16 - Prob. 92PCh. 16 - Prob. 93PCh. 16 - Prob. 94PCh. 16 - Prob. 95PCh. 16 - Prob. 96P
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