Explanation 1) Concept: We use the concept of wave motion. We can differentiate the given equation for velocity and take the ratio of displacement by velocity. At initial values of x and t, we get the equation for ϕ , plugging the given values, we get the value for phase constant. 2) Formulae: v = d y d t 3) Given: i) Angular frequency is ω = 440 r a d / s ii) Displacement y = + 4.5 m m iii) Transverse velocity is u = - 0.75 m / s iv) Wave equation is y x , t = y m s i n ⁡ ( k x - ω t + ϕ ) 4) Calculations: We know that velocity is u ( x , t ) = d y d t = d y m sin ⁡ k x - ω t + ϕ d t u ( x , t ) = - y m ω c o s ⁡ ( k x - ω t + ϕ ) We know the equation of wave y x , t = y m s i n ⁡ ( k x - ω t + ϕ ) We can take the ratio of y ( x , t ) and u ( x , t ) y x , t u x , t = y m sin ⁡ k x - ω t + ϕ - y m ω cos ⁡ k x - ω t + ϕ y

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ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Chapter 16, Problem 73P

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To find:

Phase constant ϕ

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Chapter 16, Problem 72P

Chapter 16, Problem 74P

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Chapter 16 Solutions

Fundamentals of Physics Extended

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...

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Phase constant ϕ

Solution Summary: The author explains the concept of wave motion and calculates the phase constant using x and t values.

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To find: Phase constant ϕ

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Chapter 16 Solutions

To find:

Phase constant ϕ