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Concept explainers
(a)
To show: The left hand side of the given equation is
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 50CP
The left hand side of the given equation is
Explanation of Solution
Given info: The frequency of wave is
Write the expression of the
Multiply
Integrate the above equation over on period of time
The term
The left side of the equation is,
Conclusion:
Therefore, the left hand side of the given equation is
(b)
To show: The terms of the right hand side of the given equation involving
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 50CP
The terms of the right hand side of the given equation involving
Explanation of Solution
Given info: The frequency of wave is
The part of the right hand of the equation (1) involving
Conclusion:
Therefore, the terms of the right hand side of the given equation involving
(c)
To show: The terms of the right hand side of the given equation involving
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 50CP
The terms of the right hand side of the given equation involving
Explanation of Solution
Given info: The frequency of wave is
The part of the right hand of the equation (1) involving
The integration of the
Conclusion:
Therefore, the terms of the right hand side of the given equation involving
(d)
To show: The entire right hand side of the equation reduces to
(d)
![Check Mark](/static/check-mark.png)
Answer to Problem 50CP
The entire right hand side of the equation reduces to
Explanation of Solution
Given info: The frequency of wave is
The right hand side of the equation (1) is,
The integer
Substitute
Conclusion:
Therefore, the entire right hand side of the equation reduces to
(e)
To show: The Fourier series expansion for a square wave is
(e)
![Check Mark](/static/check-mark.png)
Answer to Problem 50CP
The Fourier series expansion for a square wave is
Explanation of Solution
Given info: The frequency of wave is
The general equation of
From the part (a), The value of
From the part (d), the value of
Therefore,
Substitute
Substitute
Substitute
Conclusion:
Therefore, the Fourier series expansion for a square wave is
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Chapter 17 Solutions
Physics for Scientists and Engineers with Modern Physics
- A uniform plane wave has the generic expression Φ(z,t) = A cos(ωt – kz + δ) with the following given parameter values: wave amplitude = 10, wave frequency in Hz f = 500 Hz, phase velocity vph = 10 m/s, and the phase angle δ = 60o. Find the values of the parameters A, ω, and k. ..arrow_forwardanswer both a and b..Q23arrow_forwardIn the experiment, a mass m is attached at the opposite end of a string of linear mass density u to produce a standing wave pattern of frequency f. Complete the table of the missing numeric information. Acceleration due to gravity, g = 10 m/s². Express your answers to up to 2 significant figures. Wavelength = Linear mass density, u (in g/m) 2.0 2.0 Mass, m (gram) 45.0 16.2 meter Frequency, f (in Hz) 500arrow_forward
- Write your understanding about coherent waves. A steel wire in a piano has a length of L = 0.9m and a mass of m = 5.4 g. To what tension T must this wire be stretched so that its fundamental а. vibration possess a frequency f= 261.6 Hz? b. The equation of a plane sound wave is, y(x, t) = 6.0 × 10-6 sin(5.7x – 1500t). Find the frequency, the wavelength and the velocity of the wave. Compare the wavelength with the amplitude of the oscillations and the wave velocity with the amplitude of the velocity of the oscillations. What is the phase shift between the oscillations of two points 30.0 cm apart in the direction of the sound wave?arrow_forwardIf the periodic time of triangle wave is determined to be 10 microseconds, what is the frequency of the wave? Select one:a. 1000 Hzb. 100 Hzc. 100 kHzd. 10 kHzarrow_forwardWrite down w*w, for the following wave functions: a. W(x) = ekx b. W(x) = eAx с. Ф(x) %3D а + іx d. W(x) = cos(2TX)arrow_forward
- Consider a composite wave formed by two plane waves with slightly different frequencies of @1 = 2.7 × 10'" rad/s and w2 = 2.9 × 102 rad/s and respective wavelengths 11 17.0 nm and 12 = 16.0 nm. Calculate the wavelength of the %3D envelope wave and give your results in units of nm with 1 digit precision, rounding off to one decimal place, i.e. the nearest tenth. (time budget 6min)arrow_forwardProblem 1: A string of length 1.5 m oscillates in the standing wave pattern shown in the figure below. The string has a linear density u = acceleration due to gravity is g = 9.8 m/sec². (a) What is the speed of the waves? (b) What is the frequency of the oscillations? (c) Suppose the string continues to oscillate with the frequency you found in part (b). How many nodes will the standing wave pattern have if the suspended mass is now M 7.35 x 10-3 kg/m and the suspended mass is M 1.2 kg. The 10.8 kg? signal generator Marrow_forwardI need the diagram and complete solution answer must be in 4 decimal places.arrow_forward
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