1. Two plane waves are given by ...a. Describe the motion of the two
waves.b. At what instant is their superposition everywhere zero?c. At
what point is their superposition always zero? Get solution
2. a. Show in a phasor diagram the following two harmonic waves: ...b. Determine the mathematical expression for the resultant wave. Get solution
3. Find the resultant of the superposition of two harmonic waves in the form E = E0cos(α − ωt)with amplitudes of 3 and 4 and phases of π/6 and π/2, respectively. Both waves have a period of 1 s. Get solution
4. Two waves traveling together along the same line are given by ...Write the form of the resultant wave. Get solution
5. Plot and write the equation of the superposition of the following harmonic waves:... Get solution
6. One hundred antennas are putting out identical waves, given by E = 0.02 cos(ε − ωt) V/mThe waves are brought together at a point. What is the amplitude of the resultant when (a) all waves are in phase (coherent sources) and (b) the waves have random phase differences? Get solution
7. Two plane waves of the same frequency and with vibrations in the z-direction are given by ...Write the resultant wave form expressing their superposition at the point x − 5 cm and y = 2 cm. Get solution
8. Beginning with the relation between group velocity and phase velocity in the form vg = vp − λ(dvp/dλ)(a) express the relation in terms of n and ω and (b) determine whether the group velocity is greater or less than the phase velocity in a medium having a normal dispersion. Get solution
9. The dispersive power of glass is defined as the ratio (nF − nC)/(nD − 1), where C, D, and F refer to the Fraunhofer wavelengths, λc = 6563 Å, λD = 5890 Å, and λF = 4861 Å. Find the approximate group velocity in glass whose dispersive power is 1 /30 and for which nD = 1.50. Get solution
10. The dispersion curve of glass can be represented approximately by Cauchy’s empirical equation, n = A + B/λ2. Find the phase and group velocities for light of 500-nm wavelength in a particular glass for which A = 1.40 and B = 2.5 × 106 Å 2. Get solution
11. The dielectric constant K of a gas is related to its index of refraction by the relation K = n2.a. Show that the group velocity for waves traveling in the gas may be expressed in terms of the dielectric constant by ...where c is the speed of light in vacuum.b. An empirical relation giving the variation of K with frequency is ...where A and ω0 are constants for the gas. If the second term is very small compared to the first, show that ... Get solution
12. a. Show that group velocity can be expressed as ...b. Find the group velocity for plane waves in a dispersive medium, for which vp = A + Bλ, where A and B are constants. Interpret the result. Get solution
13. Waves on the ocean have different velocities, depending on their depth. Long-wavelength waves, traveling deep in the ocean, have a speed given approximately by ...where g is the acceleration of gravity. Short-wavelength waves, corresponding to surface ripples, have a velocity given approximately by ...where ρ is the density and T is the surface tension. Show that the group velocity for long-wavelength waves is 1/2 their phase velocity and the group velocity for short-wavelength waves is 3/2 their phase velocity. Get solution
14. A laser emits a monochromatic beam of wavelength λ, which is reflected normally from a plane mirror, receding at a speed v. What is the beat frequency between the incident and reflected light? Get solution
15. Standing waves are produced by the superposition of the wave ...and its reflection in a medium whose absorption is negligible. For the resultant wave, find the amplitude, wavelength, length of one loop, velocity, and period. Get solution
16. A medium is disturbed by an oscillation described by ...a. Determine the amplitude, frequency, wavelength, speed, and direction of the component waves whose superposition produces this result.b. What is the internodal distance?c. What are the displacement, velocity, and acceleration of a particle in the medium at x = 5 cm and t = 0.22 s? Get solution
17. Express the plane waves of Eqs. (5-19) and (5-20) in the complex representation. In this form, show that the superposition of the waves is the standing wave given by Eq. (5-22). Get solution
18. A certain argon-ion laser can support lasing over a frequency range of 6 GHz. Estimate the number of standing wave modes that might be in the laser output if the laser cavity is 1 m long. Get solution
2. a. Show in a phasor diagram the following two harmonic waves: ...b. Determine the mathematical expression for the resultant wave. Get solution
3. Find the resultant of the superposition of two harmonic waves in the form E = E0cos(α − ωt)with amplitudes of 3 and 4 and phases of π/6 and π/2, respectively. Both waves have a period of 1 s. Get solution
4. Two waves traveling together along the same line are given by ...Write the form of the resultant wave. Get solution
5. Plot and write the equation of the superposition of the following harmonic waves:... Get solution
6. One hundred antennas are putting out identical waves, given by E = 0.02 cos(ε − ωt) V/mThe waves are brought together at a point. What is the amplitude of the resultant when (a) all waves are in phase (coherent sources) and (b) the waves have random phase differences? Get solution
7. Two plane waves of the same frequency and with vibrations in the z-direction are given by ...Write the resultant wave form expressing their superposition at the point x − 5 cm and y = 2 cm. Get solution
8. Beginning with the relation between group velocity and phase velocity in the form vg = vp − λ(dvp/dλ)(a) express the relation in terms of n and ω and (b) determine whether the group velocity is greater or less than the phase velocity in a medium having a normal dispersion. Get solution
9. The dispersive power of glass is defined as the ratio (nF − nC)/(nD − 1), where C, D, and F refer to the Fraunhofer wavelengths, λc = 6563 Å, λD = 5890 Å, and λF = 4861 Å. Find the approximate group velocity in glass whose dispersive power is 1 /30 and for which nD = 1.50. Get solution
10. The dispersion curve of glass can be represented approximately by Cauchy’s empirical equation, n = A + B/λ2. Find the phase and group velocities for light of 500-nm wavelength in a particular glass for which A = 1.40 and B = 2.5 × 106 Å 2. Get solution
11. The dielectric constant K of a gas is related to its index of refraction by the relation K = n2.a. Show that the group velocity for waves traveling in the gas may be expressed in terms of the dielectric constant by ...where c is the speed of light in vacuum.b. An empirical relation giving the variation of K with frequency is ...where A and ω0 are constants for the gas. If the second term is very small compared to the first, show that ... Get solution
12. a. Show that group velocity can be expressed as ...b. Find the group velocity for plane waves in a dispersive medium, for which vp = A + Bλ, where A and B are constants. Interpret the result. Get solution
13. Waves on the ocean have different velocities, depending on their depth. Long-wavelength waves, traveling deep in the ocean, have a speed given approximately by ...where g is the acceleration of gravity. Short-wavelength waves, corresponding to surface ripples, have a velocity given approximately by ...where ρ is the density and T is the surface tension. Show that the group velocity for long-wavelength waves is 1/2 their phase velocity and the group velocity for short-wavelength waves is 3/2 their phase velocity. Get solution
14. A laser emits a monochromatic beam of wavelength λ, which is reflected normally from a plane mirror, receding at a speed v. What is the beat frequency between the incident and reflected light? Get solution
15. Standing waves are produced by the superposition of the wave ...and its reflection in a medium whose absorption is negligible. For the resultant wave, find the amplitude, wavelength, length of one loop, velocity, and period. Get solution
16. A medium is disturbed by an oscillation described by ...a. Determine the amplitude, frequency, wavelength, speed, and direction of the component waves whose superposition produces this result.b. What is the internodal distance?c. What are the displacement, velocity, and acceleration of a particle in the medium at x = 5 cm and t = 0.22 s? Get solution
17. Express the plane waves of Eqs. (5-19) and (5-20) in the complex representation. In this form, show that the superposition of the waves is the standing wave given by Eq. (5-22). Get solution
18. A certain argon-ion laser can support lasing over a frequency range of 6 GHz. Estimate the number of standing wave modes that might be in the laser output if the laser cavity is 1 m long. Get solution
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