Show that the two waves with wave functions given by E1 = 6.00 sin (100πt) and E2 = 8.00 sin (100πt 1 π/2) add to give a wave with the wave function ER sin (100πt +φ). Find the required values for ER and φ.

Show that the two waves with wave functions given by E1 = 6.00 sin (100πt) and E2 = 8.00 sin (100πt 1 π/2) add to give a wave with the wave function ER sin (100πt +φ). Find the required values for ER and φ.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter16: Electromagnetic Waves

Section: Chapter Questions

Problem 92AP: Show that the wave equation in one dimension 2fx2=1v22ft2 Is satisfied by any doubly differentiable...

See similar textbooks

Related questions

Q: For the wave y=10 sin⁡(4t/3) the frequency is 4/3 (True or False)

A: Given: A wave , y=10 sin(4t3)

Q: What is the frequency of light in the vitreous humour of the eye, where the wavelength of the light…

Q: Two waves y1 and y2 of frequency f=10 Hz and speed v=20 m/s arrive to point M with a path difference…

Q: A monochromatic (i.e., single frequency) beam of light travels from material #1 into material #2,…

A: Refractive indices n1>n2

Q: Two waves travelling in the same direction are given by: y1 = 0.2 sin(2rtx-20t+p) and y2 = 0.2…

A: According to the Bartleby guideline, only one question can be solved at one time, post the remaining…

Q: Four wave functions are given below Rank them in order of the magnitude of the period, from least to…

Q: wave of amplitude 5 m has a frequency of 40 Hz and wavelength 31.4 m. The sine wave equation for…

A: General expression for wave y=Asinωt-kx Amplitude,A=5 m Angular frequency,ω=2πf=2π40 Hz=251.3 rads

Q: In a string of length Land fixed ends we observe a system of standing waves with consecutive…

Q: Let yl and y2 be the wavefunctions of two interfering waves. In which of the listed cases, the…

Q: Consider a wave described by the wave function 6 TT 8 T TO -1 m 5 -), find the wavelength of wave? y…

Q: Two progressive waves 2л Vı(x, t) = A sin(4x – ot) and y2(x, t) = A sin( 4x – ot – X – wt - - 2…

A: Given, Wave equations, y1x,t=Asin2πλx-ωt y2x,t=Asin2πλx-ωt-π2 Amplitude, A=5 cm=0.05 m. Wavelength…

Q: Four wave functions are given below. Rank them in order of the magnitude of the frequency (f), from…

A: four wave function are given we need to Rank them in order ofmagnitude of frequencywrite the…

Q: Two identical sources of sound, both emitting waves of equal amplitude and a frequency of 2000Hz,…

A: From the general wave equation V = f*lambda , we obtain the value of the wavelength. Lambda = V/f ,…

Q: Electromagnetic radiation of intensity I0 = 380 W/m^2 passes through two parallel. Arrow slots that…

A: Given that: Io=380 W/m2d=2.8 μm=2.8×10-6 mL=1.4 my=4.6 mm=4.6×10-3 mI=55 W/m2

Q: An E&M wave has an e-field given by EĒ(x, t) = -(9.90V/m)k cos(ky + wt) and its wavelength is known…

Q: Two identical interfering waves y1 and y2 produce a resultant wave given by y_res = 0.01 sin[2(x/3 -…

Q: For the given boundary, what is the angle between the incident and reflected wave ? Free Boundary…

A: Dear student When a string wave is reflected from a free end, it reflects upright, meams there is no…

Q: For the wave y = 6 sin 2t the angular frequency is 2/3 True False

A: Given The wave equation is given as y=6 sin2t3 ...........................(1) We have to find the…

Q: 1) Pure constructive interference between two waves happens when the wavesare shifted by what…

A: Constructive interference occurs when the two waves are in phase (maxima of two waves add together)…

Q: Given V = 20 sin (50t - 10°) and I = 20 cos (50trt - 22°). Calculate the phase difference between…

Q: Consider two identical interfering waves with wavelength A = 0.4 m travelling in the positive…

A: Phase difference = k∆x = (2π/d)∆x Where d represents wavelength and ∆x represent change in position

Q: At a location that is 3.00 m from wave source A and 4.20 m from wave source B, constructive…

Q: The angle at which the wave must be transmitted in air media if the angle of reflection is 45 degree…

A: Laws of Reflection1.The incident ray, the reflected ray and the normal all lie in the same…

Q: Suppose the intensity over the surface of a hemisphere is (10 watt/ cm?). The area of the surface is…

Q: A light wire is tightly stretched with tension F. Transverse traveling waves of amplitude A and…

A: Given that, Initial power (Pi)= 0.4000 W Initial wavelength is (λ1) Final wavelength is (λ2)= 2(λ1)…

Q: Two waves travelling in the same direction are given by: y1 = 0.2 sin(3Ttx-20t+p) and y2 = 0.2…

A: Given equation is y1=0.2 sin (3πx-20t+φ_)y2=0.2 sin(3πx-20t)

Q: A pulse is traveling towards the boundary, from a less dense medium to a more dense medium. Medium1…

A: When a pulse travels from a less denser medium to more dense medium, then on reaching the boundary,…

Q: The index of refraction of a certain type of glass is expressed by the relation: 4825 nm? n(1) =…

A: Given: The wavelength (λ) of the pulse is 400 nm. The index of refraction (n) for the glass is…

Q: A plane wave of light that propagates in vacuum in the x-direction obeys the following function:…

A: Given: The equation of the wave is given as. Ex,t=2000 N/Csin1.26×107 m-1x-3.14×1015 rad/st…

Q: The Fourier transform of a function f (x) is defined as: f (w) = Lf(x)e¬iwx dx Similarly, the…

Q: D(x,t) =1.6cm sin{1.2cm(x+6.8cm/s)} Find a.wavelength B.in which direction is the wave travelling?

A: Given wave equation is D(x,t) =1.6cm sin{1.2cm(x+6.8cm/s)}. We have to find. A. Wavelength B.…

Q: If two travelling waves interfere to produce a standing wave described by: y(x,t) = 0.02…

Q: In two-source interference, the minimum intensity occurs when the phase difference is (in degrees)…

Q: Two waves that destructively interfere, resulting in a net amplitude of zero, are how many degrees…

Q: Magnetic field intensity of a propagating wave in free space is given by H =0.3 cos(4*108t+ 2y) ax…

Q: For the given boundary, what is the angle between the incident and reflected wave ? Free Boundary…

A: At open end there is reflection with zero phase change

Q: In Young's experiment, the electric fields of the waves arriving at point P are given by E1 = (5.00…

A: The electric field at point P is given as,

Q: The index of refraction of a certain type of glass is expressed by the relation: 4825 nm2 n(1) =…

A: Given data: The index of refraction of glass

Q: Please help thank you! Required info: Under favorable conditions, the human eye can detect light…

A: Given: Intensity of light wave, l=2.5×10-12 W/m2 To determine (a) At this intensity, the average…

Q: A person claps her hands while standing on the edge of a cliff overlooking a valley that is 688 m…

Q: Two waves of amplitudes 3.6 m and 4.2 m, angular frequencies 942 rad/s, propagation constants 1.57…

Q: For the given boundary, what is the angle between the incident and reflected wave ? Free Boundary…

Q: Certain blue lights have a frequencey of 6.9 x 106 Hz. What is the wavelength? O 7.85 m O 43.5 m O…

A: Given data: Frequency f=6.9×106Hz. Wavelength λ=?

Q: Suppose that the two waves in the figure have wavelength 624 nm in air. What multiple of A gives…

Q: A pulse in a more dense medium is traveling towards the boundary of a less dense medium. Medium 1…

A: In this case, the incident pulse travelling in the denser medium towards the boundary of a less…

Q: Which of the following phase shifts will result in destructive interference of two identical waves?…

A: We know that for constructive interference the path difference between them should be:- ∆x=nλ Where…

Q: Two waves of amplitude 0.3 m and 0.5 m interfere constructively. The resultant intensity is O a.0.49…

A: Given that Amplitude of 1st wave = 0.3 m Amplitude of 2nd wave = 0.5 m And they interfere…

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

Show that the two waves with wave functions given by E₁ = 6.00 sin (100πt) and E₂ = 8.00 sin (100πt 1 π/2) add to give a wave with the wave function E_R sin (100πt +φ). Find the required values for E_R and φ.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

Show that the wave equation in one dimension 2fx2=1v22ft2 Is satisfied by any doubly differentiable function of either the form f(x — vt) or f(x + vt).
Figure P24.69 shows a radio-wave transmitter and a receiver, both h = 50.0 m above the ground and d = 6.00 102 m apart. The receiver can receive signals directly from the transmitter and indirectly from signals that bounce off the ground. If the ground is level between the transmitter and receiver and a /2 phase shift occurs upon reflection, determine the longest wavelengths that interior (a) constructively and (b) destructively. Figure P24.69
Consider two waves defined by the wave functions y1(x,t)=0.50m sin(2π/3.00mx+2π/4.00s t) y1(x,t)= and y2(x,t)=0.50msin(2π/6.00mx−2π/4.00st). What are the similarities and differences between the two waves?
In Young's experiment, the electric fields of the waves arriving at point P are given by E1 = (5.00 µN/C) sin{(4.74 × 1015)t} E2 = (9.00 µN/C) sin{(4.74 × 1015)t + 21.1 rad}, where time t is in seconds. What is the amplitude of the resultant electric field at point P?
Two sources emit waves that are coherent, in phase, have wavelengths of 1.50 m, and electric field amplitudes of 2.0 N/C. Which of the following is closest to the electric field amplitude at a location 6.0 m from one source and 8.25 m from the other? Question 2 options: 4.0 N/C 3.0 N/C 2.0 N/C 1.0 N/C 0 N/C None of the other responses are correct.
The intensity of light I through a lake at a depth of x meters is given by the following formula. dI/dx=(−1.31)I (a) At what depth is the intensity of the light half that of the intensity at the surface, I0? (b) At 5 meters deep, what is the intensity of the light as a fraction of I0? c) At what depth will the intensity of the light be 11% of the light at the surface?
Show by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae-(bx-ct)^2 satisfies the wave equation: (?2?(?,?))/(?x2) = (1/v2) * (?2?(x,t))/(?t2) if the wave is given by the v = (c/b) and a, b, and c are constants.
1) Pure constructive interference between two waves happens when the wavesare shifted by what fraction of a wavelength? A) 0 B)1/6 C)1/4 D)1/3 E)1/2 2) Pure destructive interference between two waves happens when the waves areshifted by what fraction of a wavelength? A) 0 B)1/6 C)1/4 D)1/3 E)1/2
Which of the following phase shifts will result in destructive interference of two identical waves? A) 2 (lambda) B)1/4 (lambda) C)1/2 (lambda) D)(lambda) E)both c and d
For the wave y=10 sin⁡(4t/3) the frequency is 4/3 (True or False)
At a temperature of 20.0o two speakers are sending sound waves of frequency 512 Hz and 2048 Hz respectively toward a door opening of width 90.0 cm. Which wave frequency experiences a greater diffraction angle upon passing through the opening? Group of answer choices a.the 512 Hz b.the 2048 Hz c.both about the same
An E&M wave has an e-field given by E(x,t) = -(9.90 V/m)kcos(ky+wt) and its wavelength is known to be 20 micrometers. Which of the following is correct for B(x,t) and the direction of propagation? (c=3x108 m/s)