A sinusoidal wave train is described by y = 25 sin [2π (6x + 5t)] where x and y are measured in centimeters (a) What is the magnitude of the maximum transvers velocity and acceleration of the wave? (b) Determine the wavelength and the period of the wave.

A sinusoidal wave train is described by y = 25 sin [2π (6x + 5t)] where x and y are measured in centimeters (a) What is the magnitude of the maximum transvers velocity and acceleration of the wave? (b) Determine the wavelength and the period of the wave.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter18: Superposition And Standing Waves

Section: Chapter Questions

Problem 22PQ

See similar textbooks

Related questions

Q: Consider the waveform expression. y (x, t) = ymsin (639t + 4.70 + 0.163x) The transverse…

Q: Find the maximum transverse speed (in m/s) of the wave given by y= 0.005sin(0.2x-6.6t-t), where y…

Q: The wavefunction of a mechanical wave on a string is described by: y(x,t) = 0.012cos(πX-100πt+2π/3),…

Q: Find the amplitude, wave number, angular frequency, wavelength, frequency, period, wave speed and…

A: Given that, The two sinusoidal waves are as follows : f(x,t) = (1.42 m) sin (3.30 s-1 t + 2.12 m-1…

Q: The equation of a wave in the international SI system, which propagates on a string, is given by the…

A: we have for velocity of point vx,t=∂y∂t=-0.08×2π×4sin2π2x-4t

Q: A wave is described as y = 1.5 Sin[wt-kx], where k =4.04 rad/m and w =7.5 rad/sec. How far does a…

A: Given: The angular speed is w=7.5 rad/s. The wave number is k=4.04 rad/m. The time is t=11.8 s. The…

Q: A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) =…

Q: Consider the waveform expression. y (x, t) = ymsin (369t + 2.39 + 0.503x) The transverse…

A: The given waveform expression is, yx,t=ymsin369t+2.39+0.503x The general waveform expression is,…

Q: The equation of a wave in the international system SI, which propagates by a string is given by the…

A: we have yx,t=0.08cos4πx-8πt

Q: A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) =…

Q: Two sinusoidal waves travelling in the same direction with the same amplitude, wavelength, and…

A: The general equation of the wave formed when two waves of the same equation yx,t=Asinkx-ωt undergone…

Q: If y(x,t) = 0.02 sin (30x – 400t) (SI units), the period of the wave is

A: Giveny(x,t)=0.02 sin (30x-400t)comparing this equation with standardwave equation , we havey(x,t)=A…

Q: Two sinusoidal waves travelling in the same direction with the same amplitude, wavelength, and…

A: The standard equation of the wave formed when two waves undergone constructive interference is…

Q: Two waves are traveling in the same medium and described by the following wave functions: Y1 = 0.01…

Q: The wave functions of two waves traveling in the same direction are given by y1(x,t) = 0.03sin(4x +…

Q: Consider the waveform expression. y (x, t) = ymSin (2.39 + 423t + 0.435x) The transverse…

Q: Two waves travelling in the same direction are given by: y1(x,t) = 0.2 sin(3rx- 20t+T/2) and y2(x,t)…

A: Let 3πx-20t=θ. Given that:- y1=0.2sin(3πx-20t+π2)=0.2sin(π2+θ)y2=0.2sin(3πx-20t)=0.2sinθ

Q: Two sinusoidal waves of the same frequency travel in the same direction along a string. If ym1 = 3.0…

Q: Two waves traveling together along the same line are given by y, = 5 sin(@t +n/2) and y2 7 sin(wt…

Q: Two identical traveling waves, moving in the same direction, are out of phase by π/5.0 rad. What is…

Q: A traveling wave on a taut string with a tension force T, is given by the wave function: y(x,t) =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Two transverse sinusoidal waves combining in a string are described by the wave functions y1 = 0.02…

A: Given Y1 = 0.02sin(4πx+πt) Y2 = 0.02sin(4πx-πt)

Q: The equation of a transverse wave traveling along a verylong string is y = 6.0 sin(0.020px = 4.0pt),…

Q: Two sinusoidal waves are moving through a medium in the positive x-direction, both having amplitudes…

Q: For a group of waves in shallow water, wave height is measured as H=1m, and the wave celerity is…

A: The expression for the wave period(T) can be given as, T = 2πHg, where H is the wave height, g is…

Q: The vertical position, y, of any point on a rope that supports a transverse wave travelling…

A: Given terms:

Q: Two transverse sinusoidal waves combining in a string are described by the wave functions y1= 0.02…

A: For the three loops the length is given by L = 1.5 λ where, λ is the wavelength.

Q: Consider the waveform expression. y(x, t) = ymsin (3.38 + 0.163x + 207t) The transverse displacement…

A: Given:- y(x, t) = Ymsin (3.38 + 0.163x + 207t)The transverse displacement (y) of a wave is given as…

Q: The displacement of a traveling wave as a function of position and time is given by; y(x,t) = 0.165…

Q: Two sinusoidal waves travelling in the same direction with the same amplitude, wavelength, and…

A: Given: The resultant wave is yresx,t=2 cmsin4πx-60πt+π3.

Q: A transverse wave is described by the wave function y=(0.06 ?) sin[(24rad/s) t + (8.5m-1) x ]. Find…

A: From Question: The above given equation describes the : a) Amplitude , A = 0.06 m b)Angular…

Q: Transverse waves travel through a string where the tension equals 7.00 N with a speed of 20.00 m/s.…

Q: Consider a sound wave modeled with the equation s(x, t) = 4.00 nm cos (3.66 m−1 x − 1256 s−1 t).…

Q: The wave functions of two waves traveling in the same direction are given by y1(x,t) = 0.03sin(4x +…

Q: The equation of a certain time-dependent wave is y(t)= Asin(2piFt), where y(t) is the vertical…

A: The equation of a certain time-dependent wave is y(t)= Asin(2πFt), where y(t) is the vertical…

Q: A spherical wave with a wavelength of 4.1 m is emitted from the origin. At one instant of time, the…

Q: Consider a wave described by the wave function 플) -1 -1 y (x,t)=0.65m sin x + t + -m 5 3 find the…

Q: The vertical position, y, of any point on a rope that supports a transverse wave travelling…

A: standard equation of traveling wave is y=Asinωt+kx

Q: The displacement of a wave traveling in the negative x-direction is given by y(x,t)=(8.0…

Q: Two sinusoidal waves, which are identical except for a phase shift, travel along in the same…

A: The given wave equation is yRx,t=0.35cm sin6.28m-1x-1.57s-1t+π4rad ...... (I) This is…

Q: A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) =…

Q: The wavefunction of a mechanical wave on a string is described by: y(x,t) =…

Q: Two transverse sinusoidal waves combining in a string are described by the wave functions y1 = 0.02…

A: y1 = 0.02 sin3πx+πt y2 = 0.02 sin3πx-πt n = 3 L = ?

Q: The speed of a transverse wave on a string is v = 60.00 m/s and the tension in the string is FT =…

Q: In SI units a wave is represented by x = {A} cos (7.56t) . What is the time required (in s) for a…

A: The most basic equation, representing a wave is given by: x = A Cos (ωt + ϕ) , where A is the…

Q: A certain transverse wave is described by y(x,t)=Bcos[2π(xL−tτ)]y(x,t)=Bcos[2π(x/L−t/τ)],…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Two transverse sinusoidal waves combining in a string are described by the wave functions y1 = 0.02…

A: Given Y1 = 0.02sin(4πx+πt) Y2 = 0.02sin(4πx-πt)

Q: Two waves are traveling in the same medium and described by the following wave functions: Y2 = 0.01…

A: Given, wave functions: y1=0.01 msin0.3πx-20t y2=0.01 msin0.3πx-20t Comparing with general wave…

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

A sinusoidal wave train is described by y = 25 sin [2π (6x + 5t)] where x and y are
measured in centimeters (a) What is the magnitude of the maximum transvers
velocity and acceleration of the wave? (b) Determine the wavelength and the period
of the wave.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

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

Two sinusoidal waves are moving through a medium in the positive x-direction, both having amplitudes of 7.00 cm, a wave number of k=3.00 m-1, an angular frequency of =2.50 s-1, and a period of 6.00 s, but one has a phase shift of an angle =12 rad. What is the height of the resultant wave at a time t=2.00 s and a position x=0.53 m?
A sound wave in air has a pressure amplitude equal to 4.00 103 Pa. Calculate the displacement amplitude of the wave at a frequency of 10.0 kHz.
A steel wire of length 30.0 m and a copper wire of length 20.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. During what time interval will a transverse wave travel the entire length of the two wires?
A string with a mass of 0.30 kg has a length of 4.00 m. If the tension in the string is 50.00 N, and a sinusoidal wave with an amplitude of 2.00 cm is induced on the string, what must the frequency be for an average power of 100.00 W?
Two sinusoidal waves are moving through a medium in the positive x-direction, both having amplitudes of 6.00 cm, a wavelength of 4.3 m, and a period of 6.00 s, but one has a phase shift of an angle =0.50 rad. What is the height of the resultant wave at a time t=3.15 s and a position x=0.45 m ?
At t = 0, a transverse pulse in a wire is described by the function y=6.00x2+3.00 where xand y are in meters. If the pulse is traveling in the positive x direction with a speed of 4.50 m/s, write the function y(x, t) that describes this pulse.
A taut rope has a mass of 0.180 kg and a length of 3.60 m. What power must be supplied to the rope so as to generate sinusoidal waves having an amplitude of 0.100 m and a wavelength of 0.500 m and traveling with a speed of 30.0 m/s?
A cable with a linear density of =0.2 kg/m is hung from telephone poles. The tension in the cable is 500.00 N. The distance between poles is 20 meters. The wind blows across the line, causing the cable resonate. A standing waves pattern is produced that has 4.5 wavelengths between the two poles. The air temperature is T=20C . What are the frequency and wavelength of the hum?
Rank the waves represented by the following functions from the largest to the smallest according to (i) their amplitudes, (ii) their wavelengths, (iii) their frequencies, (iv) their periods, and (v) their speeds. If the values of a quantity are equal for two waves, show them as having equal rank. For all functions, x and y are in meters and t is in seconds. (a) y = 4 sin (3x 15t) (b) y = 6 cos (3x + 15t 2) (c) y = 8 sin (2x + 15t) (d) y = 8 cos (4x + 20t) (e) y = 7 sin (6x + 24t)
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?
Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is =0.075 kg/m and the tension in the string is FT=5.00 N. The time interval between instances of total destructive interference is t=0.13 s. What is the wavelength of the waves?
A 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?