- 797 step-by-step solutions
- Solved by professors & experts
- iOS, Android, & web

- Question : 1P - Complete solutions to all problems
- Question : 2P - Show that the function c(y, t) = (y - 4t) 2 is a solution of the differential wave equation. In what direction does it travel?
- Question : 3P - Consider the function c(z, t) = A (z - vt) 2 + 1 where A is a constant. Show that it is a solution of the differential wave equation. Determine the speed of the wave and the direction of propagation.
- Question : 4P - Helium-Neon lasers typically operate at a wavelength of 632.8 nm (in the red region of the visible spectrum). Determine the frequency of a beam at this wavelength.
- Question : 5P - Establish that c(y, t) = Ae-a(by - ct) 2 where A, a, b, and c are all constant, is a solution of the differential wave equation. This is a Gaussian or bell-shaped function. What is its speed and direction of travel?
- Question : 6P - How many wavelengths of a green laser (l = 532 nm) can fit into a distance equal to the thickness of a human hair (100 mm)? How far will the same number of waves extend if they originate from a microwave oven (n = 2.45 GHz)?
- Question : 7P - Find the wavelength of electromagnetic waves emitted from a 50-Hz electrical grid. Compare it with the wavelength of a 5-GHz radiation used for WiFi communication and the standard 540-THz light used in the definition of the candela.
- Question : 8P - Compute the wavelength of ultrasound waves with a frequency of 500 MHz in air. The speed of sound in air is 343 m/s.
- Question : 9P - Sitting on the end of a pier, you observe the waves washing along and notice they are very regular. Using a stopwatch, you record 20 waves passing by in 10 seconds. If when one crest washes by a column of the pier, another crest is also washing by the next column 5 meters away, with another in between, determine the period, frequency, wavelength, and speed of the wave.
- Question : 10P - Pressure waves travel through steel at about 6 km/s. What will be the wavelength of a wave corresponding to a D note (n ? 294 Hz)?
- Question : 11P - Compare the wavelengths of the A note (n = 440 Hz) played in air (v ? 343 m/s) and water (v ? 1500 m/s).
- Question : 12P - A 20-Hz vibrator is activated at one end of a 6-m-long string. The first disturbance reaches the other end of the string in 1.2 s. How many wavelengths will fit on the string?
- Question : 13P - Show that for a periodic wave v = (2p>l)v.
- Question : 14P - Make up a table with columns headed by values of u running from -p>2 to 2p in intervals of p>4. In each column place the corresponding value of sin u, beneath those the values of cos u, beneath those the values of sin (u - p>4), and similarly with the functions sin (u - p>2), sin (u - 3p>4), and sin (u + p>2). Plot each of these functions, noting the effect of the phase shift. Does sin u lead or lag sin (u - p>2). In other words, does one of the functions reach a particular magnitude at a smaller value of u than the other and therefore lead the other (as cos u leads sin u)?
- Question : 15P - Make up a table with columns headed by values of kx running from x = -l>2 to x = +l in intervals of x of l>4
- Question : 16P - Make up a table with columns headed by values of vt running from t = -t>2 to t = +t in intervals of t of t>4
- Question : 17P - The profile of a transverse harmonic wave, travelling at 2.5 m/s on a string, is given by y = (0.1 m)sin (0.707 m-1 ) x. Determine its wavelength, period, frequency, and amplitude
- Question : 18P - Figure P.2.18 represents the profile (t = 0) of a transverse wave on a string traveling in the positive x-direction at a speed of 20.0 m>s. (a) Determine its wavelength. (b) What is the frequency of the wave? (c) Write down the wavefunction for the disturbance. (d) Notice that as the wave passes any fixed point on the x-axis the string at that location oscillates in time. Draw a graph of the c versus t showing how a point on the rope at x = 0 oscillates.
- Question : 19P - Figure P.2.19 represents the profile (t = 0) of a transverse wave on a string traveling in the positive z-direction at a speed of 100 cm>s. (a) Determine its wavelength. (b) Notice that as the wave passes any fixed point on the z-axis the string at that location oscillates in time. Draw a graph of c versus t showing how a point on the rope at x = 0 oscillates. (c) What is the frequency of the wave?
- Question : 20P - A transverse wave on a string travels in the negative y-direction at a speed of 40.0 cm>s. Figure P.2.20 is a graph of c versus t showing how a point on the rope at y = 0 oscillates. (a) Determine the wave
- Question : 21P - Given the wavefunctions c1 = 5 sin 2p(0.4x + 2t) and c2 = 2 sin (5x - 1.5t) determine in each case the values of (a) frequency, (b) wavelength, (c) period, (d) amplitude, (e) phase velocity, and (f) direction of motion. Time is in seconds and x is in meters.
- Question : 22P - The wavefunction of a transverse wave on a string is c(x, t) = (0.2 m) cos 2p[(4 rad/m)x - (20 Hz)t] Determine the (a) frequency, (b) period, (c) amplitude, (d) wavelength, (e) phase velocity, and (f) direction of travel of this function.
- Question : 23P - A wave is given in SI units by the expression c(y, t) = (0.25) sin 2pa y 2 + t 0.05b Find its (a) wavelength, (b) period, (c) frequency, (d) amplitude, (e) phase velocity, and (f) direction of propagation.
- Question : 24P - Show that c(x, t) = Asin k(x - vt) [2.13] is a solution of the differential wave equation.
- Question : 25P - Show that c(x, t) = Acos(kx - vt) is a solution of the differential wave equation.
- Question : 26P - Express the wavefunction c(x, t) = Acos(kx - vt) using the sine function.
- Question : 27P - Show that if the displacement of the string in Fig. 2.12 is given by y(x, t) = Asin [kx - vt + e] then the hand generating the wave must be moving vertically in simple harmonic motion.
- Question : 28P - Write the expression for the wavefunction of a harmonic wave of amplitude 103 V>m, period 2.2 * 10-15 s, and speed 3 * 108 m>s. The wave is propagating in the negative x-direction and has a value of 103 V>m at t = 0 and x = 0.
- Question : 29P - Consider the pulse described in terms of its displacement at t = 0 by y(x, t)? t = 0 = C 2 + x2 where C is a constant. Draw the wave profile. Write an expression for the wave, having a speed v in the negative x-direction, as a function of time t. If v = 1 m>s, sketch the profile at t = 2 s.
- Question : 30P - Determine the magnitude of the wavefunction c(z, t) = Acos [k(z + vt) + p] at the point z = 0, when t = t>2 and when t = 3p>4.
- Question : 31P - Which of the following is a valid wavefunction? (a) c1 = A(x + at) (b) c2 = A(y - bt2 ) (c) c3 = A(kx - vt + p) The quantities A, a, b, and k are positive constants.
- Question : 32P - Use Eq. (2.32) to calculate the phase velocity of a wave whose representation in SI units is c(z, t) = Acosp(2 * 104 z - 6 * 1012t)
- Question : 33P - The displacement of a wave on a vibrating string is given by c(y, t) = (0.050m)sin 2pa y l + t t b where the wave travels at 20m>s and it has a period of 0.10 s. What is the displacement of the string at y = 2.58m and time a t = 3.68 s?
- Question : 34P - Begin with the following theorem: If z =
- Question : 35P - Using the results from Problem 2.34, show that for a wave with a phase w(x, t) = k(x - vt) we can determine the speed by setting dw>dt = 0. Apply the technique to Problem 2.32.
- Question : 36P - A Gaussian wave has the form c(x, t) = Ae-a(bx+ct) 2 . Use the fact that c(x, t) =
- Question : 37P - Create an expression for the profile of a harmonic wave traveling in the z-direction whose magnitude at z = -l>12 is 0.866, at z = +l>6 is 1>2, and at z = l>4 is 0.
- Question : 38P - Which of the following expressions correspond to traveling waves? For each of those, what is the speed of the wave? The quantities a, b, and c are positive constants. (a) c(z, t) = (az - bt) 2 (b) c(x, t) = (ax + bt + c) 2 (c) c(x, t) = 1>(ax2 + b)
- Question : 39P - Determine which of the following describe traveling waves: (a) c(y, t) = e-(a2 y2+b2 t 2-2abty) (b) c(z, t) = Asin (az2 - bt2 ) (c) c(x, t) = Asin 2pa x a + t b b 2 (d) c(x, t) = Acos2 2p(t - x) Where appropriate, draw the profile and find the speed and direction of motion.
- Question : 40P - Given the traveling wave c(x, t) = 5.0 exp (-ax2 - bt2 - 21ab xt), determine its direction of propagation. Calculate a few values of c and make a sketch of the wave at t = 0, taking a = 25 m-2 and b = 9.0 s-2 . What is the speed of the wave?
- Question : 41P - What is the phase difference of a sound wave between two points 20 cm apart (extending directly in a line from a speaker) when the A note (v = 440 Hz) is played? The speed of sound is v = 343 m/s.
- Question : 42P - Consider orange light with a frequency of 5 * 1014 Hz and a phase velocity of 3 * 108 m>s. Find the shortest distance along the wave between two points having a phase difference of 180
- Question : 43P - Write an expression for the wave shown in Fig. P.2.43. Find its wavelength, velocity, frequency, and period.
- Question : 44P - Working with exponentials directly, show that the magnitude of c = Aeivt is A. Then rederive the same result using Euler
- Question : 45P - Show that the imaginary part of a complex number z
- Question : 46P - Take the complex quantities z
- Question : 47P - Take the complex quantities z
- Question : 48P - Beginning with Eq. (2.51), verify that c(x, y, z, t) = Aei[k(ax +by +gz) ? vt] and that a2 + b2 + g2 = 1 Draw a sketch showing all the pertinent quantities.
- Question : 49P - Show that Eqs. (2.64) and (2.65), which are plane waves of arbitrary form, satisfy the three-dimensional differential wave equation.
- Question : 50P - The electric field of an electromagnetic plane wave is given in SI units by E$ = E$0ei(3x- 22 y -9.9*108 t)(a) What is the wave
- Question : 51P - Consider the function c(z, t) = Aexp [-(a2 z 2 + b2 t 2 + 2abzt)] where A, a, and b are all constants, and they have appropriate SI units. Does this represent a wave? If so, what is its speed and direction of propagation?
- Question : 52P - De Broglie
- Question : 53P - Write an expression in Cartesian coordinates for a harmonic plane wave of amplitude A and frequency v propagating in the direction of the vector k$, which in turn lies on a line drawn from the origin to the point (4, 2, 1). [Hint: First determine k$ and then dot it with $ r.]
- Question : 54P - Write an expression in Cartesian coordinates for a harmonic plane wave of amplitude A and frequency v propagating in the positive x-direction.
- Question : 55P - Show that c($k ~$ r, t) may represent a plane wave where k$ is normal to the wavefront. [Hint: Let $ r1 and $ r2 be position vectors drawn to any two points on the plane and show that c($ r1, t) = c($ r2, t).]
- Question : 56P - Show explicitly, that the function c($ r, t) = Aexp [i(k$~$ r + vt + e)] describes a wave provided that v = v>k.
- Question : 57P - Make a table with the columns headed by u running from -p to 2p in intervals of p>4. In each column place the corresponding value of sin u and beneath those the values of sin (u + p>2). Next add these, column by column, to yield the corresponding values of the function sin u + sin (u + p>2). Plot the three functions and make some observations.
- Question : 58P - Make a table with the columns headed by u running from -p to 2p in intervals of p>4. In each column place the corresponding value of sin u and beneath those the values of sin (u - 3p>4). Next add these, column by column, to yield the corresponding values of the function sin u + sin (u - 3p>4). Plot the three functions and make some observations.
- Question : 59P - Two waves with equal frequencies and amplitudes arrive at the same point in space. At t = 0, the wavefunction of the first wave is c1(t) = A sinvt and the second wave
- Question : 60P - Make up a table with columns headed by values of kx running from x = -l>2 to x = +l in intervals of x of l>4. In each column place the corresponding values of cos kx and beneath that the values of cos(kx + p). Next plot the three functions cos kx, cos(kx + p), and cos kx + cos(kx + p).

5out of 5Joshua L LandowThe Optics, Global Edition 5th edition Solutions Manual Was amazing as it had almost all solutions to textbook questions that I was searching for long. I would highly recommend their affordable and quality services.

5out of 5Sorekokazeb42The Optics, Global Edition Optics, Global Edition Solutions Manual Was amazing as it had almost all solutions to textbook questions that I was searching for long. I would highly recommend their affordable and quality services.

5out of 5GettinghungupI am a student at Harvard University and I read Optics, Global Edition Solutions Manual and attempted crazy for study textbook solutions manuals which helped me a lot. Thanks a lot.

5out of 5AntonioThe Optics, Global Edition Solutions Manual Was amazing as it had almost all solutions to textbook questions that I was searching for long. I would highly recommend their affordable and quality services.

5out of 5Josh KerbyI have taken their services earlier for textbook solutions which helped me to score well. I would prefer their Optics, Global Edition Solutions Manual For excellent scoring in my academic year.

5out of 5DanaI have read their books earlier and this new edition Optics, Global Edition helped me in providing textbook solutions. I prefer to avail their services always as they are consistent with their quality.