Explanation 1) Concept: We use the concept power of wave which involves linear mass density, velocity, angular velocity and amplitude. Using this equation, we can find the relation between power and tension and frequency. Then, we can find the new power in terms of initial power by taking the ratio. 2) Formulae: P = 1 2 μ v ω 2 y m 2 3) Calculations: a) New energy transmission P 2 in terms of P 1 if the tension is increased to τ 2 = 4 τ 1 : P = 1 2 μ v ω 2 y m 2 We know velocity on string is v = τ μ and ω = 2 π f Plugging the values we get, P = 1 2 μ τ μ 2 π f 2 y m 2 We can write = μ × μ , we get, P = 1 2 μ τ 4 π 2 f 2 y m 2 Here, τ and f are the variables and the remaining terms are constant terms, so the power is directly proportional to the tension and frequency. We can write, P 1 = 1 2 μ τ 1 4 π 2 f 2 y m 2 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … . ( 1 ) P 2 = 1 2 μ τ 2 4 π 2 f 2 y m 2 Since τ 2 = 4 τ 1 , we can write, P 2 = 1 2 μ 4 τ 1 4 π 2 f 2 y m 2 … … … … … … … … … … … … … … … … … … … … … … … … … … . … … . ( 2 ) Taking the ratio of P 2 P 1 using equations (1) and (2) we get, P 2 P 1 = 1 2 μ 4 τ 1 4 π 2 f 2 y m 2 1 2 μ τ 1 4 π 2 f 2 y m 2 P 2 P 1

10th Edition

ISBN: 9781118230718

Author: David Halliday

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Concept explainers

Electromagnetic Waves

Electromagnetic waves are waves that consist of magnetic field and electric field components perpendicular to each other. These field components are also perpendicular to the direction of propagation of the wave.

Question

Chapter 16, Problem 74P

To determine

To find:

a) New energy transmission P2 in terms of P1 if the tension is increased to τ2=4τ1.

b) New energy transmission P2 in terms of P1 if the frequency is increased to f2=f1/2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 73P

Chapter 16, Problem 75P

Students have asked these similar questions

Question 3 of 17 L X L L T 0.5/ In the figure above, three uniform thin rods, each of length L, form an inverted U. The vertical rods each have a mass m; the horizontal rod has a mass 3m. NOTE: Express your answer in terms of the variables given. (a) What is the x coordinate of the system's center of mass? xcom L 2 (b) What is the y coordinate of the system's center of mass? Ycom 45 L X Q Search MD bp N

Sketch the harmonic on graphing paper.

Exercise 1: (a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre- sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case j = 1. (b) Verify that they satisfy the so(3) Lie algebra commutation relation: [D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h). (c) Prove the identity 3 Dm'm,(Î²) = Σ (D(Î¡)D(Î¡))m'¡m; · i=1

Chapter 16 Solutions

Fundamentals of Physics

Ch. 16 - Prob. 1Q Ch. 16 - Prob. 2Q Ch. 16 - Prob. 3Q Ch. 16 - Prob. 4Q Ch. 16 - Prob. 5Q Ch. 16 - The amplitudes and phase differences for four...Ch. 16 - Prob. 7Q Ch. 16 - a If a standing wave on a siring is given by y't =...Ch. 16 - Prob. 9Q Ch. 16 - If you set up the seventh harmonic on a string, a...

Ch. 16 - Prob. 11Q Ch. 16 - If a wave yx, t = 6.0mm sinkx 600 rad/st ...Ch. 16 - Prob. 2P Ch. 16 - A wave has an angular frequency of 110 rad/s and a...Ch. 16 - Prob. 4P Ch. 16 - A sinusoidal wave travels along a string. The time...Ch. 16 - Prob. 6P Ch. 16 - A transverse sinusoidal wave is moving along a...Ch. 16 - Prob. 8P Ch. 16 - Prob. 9P Ch. 16 - The equation of a transverse wave traveling along...Ch. 16 - Prob. 11P Ch. 16 - GO The function yx, t = 15.0 cm cosx 15 t, with x...Ch. 16 - Prob. 13P Ch. 16 - The equation of a transverse wave on a string is y...Ch. 16 - Prob. 15P Ch. 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. 18P Ch. 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 - SSM ILW A sinusoidal transverse wave is traveling...Ch. 16 - Prob. 24P 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. 27P 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 - Use the wave equation to find the speed of a wave...Ch. 16 - Prob. 31P Ch. 16 - What phase difference between two identical...Ch. 16 - Prob. 33P Ch. 16 - Prob. 34P Ch. 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. 41P Ch. 16 - Prob. 42P Ch. 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. 45P Ch. 16 - String A is stretched between two clamps separated...Ch. 16 - Prob. 47P Ch. 16 - If a transmission line in a cold climate collects...Ch. 16 - Prob. 49P Ch. 16 - Prob. 50P Ch. 16 - Prob. 51P Ch. 16 - A rope, under a tension of 200 N and fixed at both...Ch. 16 - Prob. 53P Ch. 16 - Prob. 54P Ch. 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 - GO In Fig. 16-42, a string, tied to a sinusoidal...Ch. 16 - GO In Fig. 16-43, an aluminum wire, of length L1 =...Ch. 16 - Prob. 60P Ch. 16 - Prob. 61P Ch. 16 - Prob. 62P Ch. 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. 66P Ch. 16 - Prob. 67P Ch. 16 - Prob. 68P Ch. 16 - Prob. 69P Ch. 16 - Prob. 70P Ch. 16 - A transverse sinusoidal wave is generated at one...Ch. 16 - Prob. 72P Ch. 16 - Prob. 73P Ch. 16 - Prob. 74P Ch. 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. 77P Ch. 16 - Prob. 78P Ch. 16 - Prob. 79P Ch. 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. 83P Ch. 16 - Prob. 84P Ch. 16 - Prob. 85P Ch. 16 - a Write an equation describing a sinusoidal...Ch. 16 - A wave on a string is described by yx, t = 15.0...Ch. 16 - Prob. 88P Ch. 16 - Two waves are described by...Ch. 16 - Prob. 90P Ch. 16 - SSM In a demonstration, a 1.2 kg horizontal rope...Ch. 16 - Prob. 92P Ch. 16 - A traveling wave on a string is described by...Ch. 16 - Prob. 94P Ch. 16 - Prob. 95P Ch. 16 - Consider a loop in the standing wave created by...

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.

a) New energy transmission P 2 in terms of P 1 if the tension is increased to τ 2 = 4 τ 1 . b) New energy transmission P 2 in terms of P 1 if the frequency is increased to f 2 = f 1 / 2 .

Solution Summary: The author explains the concept power of wave, which involves linear mass density, velocity, angular velocity and amplitude.

Concept explainers

To find:

a) New energy transmission P2 in terms of P1 if the tension is increased to τ2=4τ1.

b) New energy transmission P2 in terms of P1 if the frequency is increased to f2=f1/2.

Want to see the full answer?

Chapter 16 Solutions

a) New energy transmission P 2 in terms of P 1 if the tension is increased to τ 2 = 4 τ 1 . b) New energy transmission P 2 in terms of P 1 if the frequency is increased to f 2 = f 1 / 2 .

Solution Summary: The author explains the concept power of wave, which involves linear mass density, velocity, angular velocity and amplitude.

Concept explainers

To find: a) New energy transmission P2 in terms of P1 if the tension is increased to τ2=4τ1. b) New energy transmission P2 in terms of P1 if the frequency is increased to f2=f1/2.

Want to see the full answer?

Chapter 16 Solutions

To find:

a) New energy transmission P2 in terms of P1 if the tension is increased to τ2=4τ1.

b) New energy transmission P2 in terms of P1 if the frequency is increased to f2=f1/2.