Essay : Compare the wave function y (x,t) using sine and cosine functions. State their similarities and differences concerning the wave parameters : direction of motion , amplitude , frequency , period , wavelength , angular frequency , speed and wave number . Support your answer by Illustrating the salient points/parameters using graph/diagram of sinusoidal wave.

Essay : Compare the wave function y (x,t) using sine and cosine functions. State their similarities and differences concerning the wave parameters : direction of motion , amplitude , frequency , period , wavelength , angular frequency , speed and wave number . Support your answer by Illustrating the salient points/parameters using graph/diagram of sinusoidal wave.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter17: Traveling Waves

Section: Chapter Questions

Problem 16PQ: A harmonic transverse wave function is given by y(x, t) = (0.850 m) sin (15.3x + 10.4t) where all...

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Compare the wave function y (x,t) using sine and cosine functions. State their similarities and differences concerning the wave parameters : direction of motion , amplitude , frequency , period , wavelength , angular frequency , speed and wave number . Support your answer by Illustrating the salient points/parameters using graph/diagram of sinusoidal wave.
A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s in case the value of amplitude A corresponds to the first letter of your name: letter E A. A=0.1 mB. A=0.15 mC. A=0.2 mÇ. A=0.25 mD. A=0.3 mDh. A=0.35 mE. A=0.4 mË. A=0.45 mF. A=0.5 m G. A=0.55 mGj. A=0.6 mH. A=0.65 mI. A=0.7 mJ. A=0.75 mK. A=0.8 mL. A=0.85 mLl. A=0.9 mM. A=0.95 m N. A=1.05 mNj. A= 1.1 mO. A=1.15 mP. A=1.2 mQ. A=1.25 mR. A=1.3 mRr. A=1.35 mS. A=1.4 mSh. A=1.45 m T. A=1.5 mTh. A=1.55 mU. A=1.6 mV. A=1.65 mX. A=1.7 mXh. A=1.75 mY. A=1.8 mZ. A=1.85 mZh. A=1.9 m 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results?…
A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the amplitude is A= 1.3m 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) 5. Find the resultant wave function analytically. 6. Study how the resulting wave…
A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the value of amplitude A=0.4m. 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) 5. Find the resultant wave function analytically. 6. Study how the resulting…
A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the value of amplitude A=0.4m. 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer.
Questions 1-6: Consider a wave on a string that can be described by the following equation: y (x, t) = 2.5 cm Sin(2.0 m-1x + 1800 s-1- 4.7) %3D 1. This is describes a... [circle one] ( sanding wave / wave traveling toward +x/wave traveling towards -x) 2. Amplitude = 3. Wavelength = 4. Frequency = 5. Wave speed% = 6. Speed of the medium att = 2.0 ms = X-0.25m
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. ..
The wave function for a travelling wave on a taut string is: (SI units) y(x,t)=0.05 sen (4πx — 8πt) 1. Determine the characteristic magnitudes of the wave (amplitude, angular frequency, wave number, wavelength, frequency, period, propagation velocity) 2. Derive the general expressions for the velocity and transversal acceleration of a element of the chord and its maximum values. 3. Determine the values of the elongation, velocity and acceleration of a point located 1 m from the origin at time t = 3 s
A wave produced by the superposition of two harmonic waves is described by the equation y(x,t) = 5 cos(2 x - 2 t) sin(3 x - 8 t) where all quantities are in SI units. a) What is the phase velocity of the wave Number b) What is the group velocity of the wave Number c) Does the wave display normal or anomalous dispersion? O normal O anomalous
Consider the sinusoidal traveling wave shown in the figure (this is a snapshot at a certain instant of time). Assume the wave travels at 1.0 m/s. a) What is the wave's amplitude? b) What is its wavenumber k? c) What is its angular velocity w? d) What is its period T? e) What is its frequency f?
Solve the following problems. Write your answers with its corresponding solutions in a separate sheet of paper. 1. The wave function that describes a certain transverse wave at initial time t=0 is yk, t-(7.20mm)sin2n( lasm a.0400 s Find the wave's (a) amplitude, (b) wavelength, (c) frequency, (d) speed of propagation, (e) period, (f) wave number, and (g) direction of propagation.
Consider the surface density wave 01 = 010e (w+30-ar³/4) where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of the wave. 01 1. Using mathematical arguments show whether the pattern described by σ₁ is rotating clockwise or anticlockwise. 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral.