Essential University Physics: Volume 1 (3rd Edition)
3rd Edition
ISBN: 9780321993724
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 14, Problem 53P
To determine
To show: The superposition of the given wave is also a harmonic wave and to determine the amplitude as a function of the phase difference.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A standing wave is the result of superposition of two harmonic waves given by the equations y1(x;t) =Asin(ωt - kx) and y2(x; t) = Asin(ωt + kx). The angular frequency is ω = 3π rad/s and the k = 2πrad/m is the wave number.(a) Give an expression for the amplitude of standing wave.
b) calculate the frequency of the wave
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.
..
Can you solve it plz and explain it please
Chapter 14 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Ch. 14.1 - A boat bobs up and down on a water wave, moving 2...Ch. 14.2 - The figure shows snapshots of two waves...Ch. 14.3 - Two identical stars are different distances from...Ch. 14.4 - Your band needs a new guitar amplifier, and the...Ch. 14.5 - Light shines through two small holes into a dark...Ch. 14.6 - Youre holding one end of a taut rope, and you cant...Ch. 14.7 - A string 1 m long is clamped tightly at one end...Ch. 14.8 - In Fig. 14.35, which is moving faster in relation...Ch. 14 - What distinguishes a wave from an oscillation?Ch. 14 - Red light has a longer wavelength than blue light....
Ch. 14 - Prob. 3FTDCh. 14 - As a wave propagates on a string, the string moves...Ch. 14 - If you doubled the tension in a string, what would...Ch. 14 - A heavy cable is hanging vertically, its bottom...Ch. 14 - Prob. 7FTDCh. 14 - Medical ultrasound uses frequencies around 107 Hz,...Ch. 14 - If you double the pressure of a gas while keeping...Ch. 14 - Water is about a thousand times more dense than...Ch. 14 - Prob. 11FTDCh. 14 - When a wave source moves relative to the medium, a...Ch. 14 - Why can a boat easily produce a shock wave on the...Ch. 14 - Ocean waves with 18-m wavelength travel at 5.3...Ch. 14 - Prob. 15ECh. 14 - Prob. 16ECh. 14 - Prob. 17ECh. 14 - A seismograph located 1250 km from an earthquake...Ch. 14 - Medical ultrasound waves travel at about 1500 m/s...Ch. 14 - An ocean wave has period 4.1 s and wavelength 10.8...Ch. 14 - Find the (a) amplitude, (b) wavelength, (c)...Ch. 14 - Ultrasound used in a medical imager has frequency...Ch. 14 - Prob. 23ECh. 14 - Prob. 24ECh. 14 - Prob. 25ECh. 14 - A transverse wave 1.2 cm in amplitude propagates...Ch. 14 - A transverse wave with 3.0-cm amplitude and 75-cm...Ch. 14 - Prob. 28ECh. 14 - Prob. 29ECh. 14 - Show that P/ from Equation 14.9 has the units of...Ch. 14 - Find the sound speed in air under standard...Ch. 14 - Timers in sprint races start their watches when...Ch. 14 - The factor for nitrogen dioxide (NO2) is 1.29....Ch. 14 - A gas with density 1.0 kg/m3 and pressure 81 kN/m2...Ch. 14 - Prob. 35ECh. 14 - Youre flying in a twin-engine turboprop aircraft,...Ch. 14 - Prob. 37ECh. 14 - A 2.0-m-long string is clamped at both ends. (a)...Ch. 14 - When a stretched string is clamped at both ends,...Ch. 14 - A string is clamped at both ends and tensioned...Ch. 14 - A crude model of the human vocal tract treats it...Ch. 14 - A car horn emits 380-Hz sound. If the car moves at...Ch. 14 - A fire stations siren is blaring at 85 Hz. Whats...Ch. 14 - A fire trucks siren at rest wails at 1400 Hz;...Ch. 14 - Red light emitted by hydrogen atoms at rest in the...Ch. 14 - Figure 14.36 shows a simple harmonic wave at time...Ch. 14 - Prob. 47PCh. 14 - Prob. 48PCh. 14 - Figure 14.37 shows a wave train consisting of two...Ch. 14 - A loudspeaker emits energy at the rate of 50 W,...Ch. 14 - Prob. 51PCh. 14 - Prob. 52PCh. 14 - Prob. 53PCh. 14 - A wire is under 32.8-N tension, carrying a wave...Ch. 14 - A spring of mass m and spring constant k has an...Ch. 14 - Prob. 56PCh. 14 - Prob. 57PCh. 14 - Figure 14.38 shows two observers 20 m apart on a...Ch. 14 - An ideal spring is stretched to a total length L1....Ch. 14 - Prob. 60PCh. 14 - You see an airplane 5.2 km straight overhead....Ch. 14 - What are the intensities in W/m2 of sound with...Ch. 14 - Show that a doubling of sound intensity...Ch. 14 - Sound intensity from a localized source decreases...Ch. 14 - At 2.0 in from a localized sound source you...Ch. 14 - The A-string (440 Hz) on a piano is 38.9 cm long...Ch. 14 - Prob. 67PCh. 14 - Youre designing an organ for a new concert hall;...Ch. 14 - Show by differentiation and substitution that a...Ch. 14 - Prob. 70PCh. 14 - Youre a marine biologist concerned with the effect...Ch. 14 - A 2.25-m-long pipe has one end open. Among its...Ch. 14 - Prob. 73PCh. 14 - Obstetricians use ultrasound to monitor fetal...Ch. 14 - Prob. 75PCh. 14 - You move at speed u toward a wave source thats...Ch. 14 - Youre a meteorologist specifying a new Doppler...Ch. 14 - Use a computer to form the sum implied in the...Ch. 14 - Your little sister and her friend build treehouses...Ch. 14 - An airport neighborhood is concerned about the...Ch. 14 - Tsunamis are ocean waves generally produced when...Ch. 14 - Tsunamis are ocean waves generally produced when...Ch. 14 - Tsunamis are ocean waves generally produced when...Ch. 14 - Tsunamis are ocean waves generally produced when...
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
- The equation of a harmonic wave propagating along a stretched string is represented by y(x, t) = 4.0 sin (1.5x 45t), where x and y are in meters and the time t is in seconds. a. In what direction is the wave propagating? be. N What are the b. amplitude, c. wavelength, d. frequency, and e. propagation speed of the wave?arrow_forwardTwo sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle . What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [Hint: Use the trig identity sinu+sinv=2sin(u+v2)cos(uv2)arrow_forwardA harmonic transverse wave function is given by y(x, t) = (0.850 m) sin (15.3x + 10.4t) where all values are in the appropriate SI units. a. What are the propagation speed and direction of the waves travel? b. What are the waves period and wavelength? c. What is the amplitude? d. If the amplitude is doubled, what happens to the speed of the wave?arrow_forward
- Consider two waves defined by the wave functions y1(x,t)=0.50msin(23.00mx+24.00st) and y2(x,t)=0.50msin(26.00mx24.00st) . What are the similarities and differences between the two waves?arrow_forwardConsider a composite wave formed by two plane waves with slightly different frequencies of 0, = 2.7 x 1012 rad/s and aw2 = 2.9 × 1012 rad/s and respective wavelengths A1 = 17.0 nm and 2 16.0 nm. Calculate the propagation velocity %D of the envelope wave and give your results in units of m/s with 1 digit precision, rounding off to one decimal place, i.e. the nearest tenth. (time budget 5min)arrow_forwardTwo harmonic waves are described by Yı = A sin(3x– 5t), Y2 = A sin(3 x – 5t – 4). A = 3.2 m, with x and t in SI units and th phase angle in radians. What is the displacement of the sum y1+ of these two harmonic waves at x = 1 m an t = 1 s?arrow_forward
- Consider two wave functions y1 (x, t) = A sin (kx − ωt) and y2 (x, t) = A sin (kx + ωt + ϕ). The resultant wave form when you add the two functions is yR = 2A sin (kx +ϕ/2) cos (ωt + ϕ/2). Consider the case where A = 0.03 m−1, k = 1.26 m−1, ω = π s−1 , and ϕ = π/10 . (a) Where are the first three nodes of the standing wave function starting at zero and moving in the positive x direction? (b) Using a spreadsheet, plot the two wave functions and the resulting function at time t = 1.00 s to verify your answer.arrow_forwardGiven the wave functions y1 (x, t) = A sin (kx − ωt) and y2 (x, t) = A sin (kx − ωt + ϕ) with ϕ ≠ π/2 , show that y1 (x, t) + y2 (x, t) is a solution to the linear wave equation with a wave velocity of v = √(ω/k).arrow_forward6:18 Consider a composite wave formed by two plane waves with slightly different frequencies of 0 = 2.7 x 10" rad/s and o, = 2.9 x 10' rad/s and respective wavelengths A = 17.0 nm and A, = 16.0 nm. Calculate the propagation velocity of the carrier wave and give your results in units of m/s with 1 digit precision, rounding off to one decimal place, i.e. the nearest tenth. (time budget 5min)arrow_forward
- Problem 4: A traveling wave along the x-axis is given by the following wave functionψ(x, t) = 3.6 cos(1.4x - 9.2t + 0.34),where x in meter, t in seconds, and ψ in meters. Read off the appropriate quantities for this wave function and find the following characteristics of this plane wave: Part (a) The amplitude in meters. Part (b) The frequency, in hertz. Part (c) The wavelength in meters. Part (d) The wave speed, in meters per second. Part (e) The phase constant in radians.arrow_forwardy2 = 0.01 sin(5rx+40rt), O y1 = 0.04 sin(20x-320nt); y2 = 0.04 sin(20TDX-+320rt), Two sinusoidal waves of wavelengthA = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the form: O y res (x,t) = 12(cm) cos(p/2) sin(3ttx+150rtt+p/2). O y_res (x,t) = 12(cm) cos(p/2) sin(3nx-180nt+p/2). y_res (x,t) = 12(cm) cos(p/2) sin(3nx-150nt+p/2). O y res (x,t) = 12(cm) cos(p/2) sin(150rtx-3nt+p/2). y_res (x,t) = 12(cm) cos(@/2) sin(150tx+3nt+p/2). Two identical sinusoidal waves with wavelengths of 1.5 m travel in the same. direction at a speed of 10 m/s. If the two waves originate from the same startingarrow_forwardOn a real string of linear density μ, some of the energy of the wave dissipates as the wave travels down the string. Such a situation can be described by a wave function y (x, t) whose amplitude A(x) depends on the position x, by y (x, t) = A(x) sin(kx – wot), where A(x) = (Age¯b¾, for constant values AQ and b. Derive an expression for the average power P(x) transported by the wave as a function of x, where x > 0. P(x) =arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning