A wave traveling along a string is described by f (x, t) = a sin (abx + qt)with a = 30.0 mm, b = 0.3 m1 and q = 10.5 s1.Calculate(a) (:(b)(c)(d)(ethe amplitude (in m),the wavelength (in m),the period (in s).and speed of the wave (m/s).Compute the y component of the displacement of the string (in m) at x= 0.5 m and t= 1.60 s.

As per guidelines , only 3 subparts are solved here. Given, A wave travelling along a string is…

A wave traveling along a string is described by f (x, t) = a sin (abx + qt) 30.0 mm, b 0.3 m1 and q 10.5 s1. with a %3D %3D Calculate (a) (: (b) (c) the amplitude (in m), the wavelength (in m). the period (in s),

A wave traveling along a string is described by f (x, t) = a sin (abx + qt) 30.0 mm, b 0.3 m1 and q 10.5 s1. with a %3D %3D Calculate (a) (: (b) (c) the amplitude (in m), the wavelength (in m). the period (in s),

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter13: Mechanical Waves

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: At time t = 0 and at position x = 0 m along a string, a travelingsinusoidal wave with an angular…

A: The general form of the wave is given by,

Q: Two sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase…

A: Given that Wavelength λ = 23m Amplitude A = 6 cm Velocity V = 50 m/s

Q: A steel wire with mass 25.4 g and length 1.30 m is strung on a bass so that the distance from the…

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

Q: The equation of a standing wave is y(x,t) = 0.8 cos(0.1tx) sin(200tt) %3D where x and y are in cm…

A: The expression for the general form of the standing wave is given as y=2acoskxsinωt On comparing…

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

Q: The wavefunction of a mechanical wave on a string is described by: y(x,t) = 0.012sin(Ttx-…

Q: a wave is represented by y=(3.00m)sin(2.5t-3,14x). find the (a) amplitude, (b) angular velocity, (c)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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

Q: Two sinusoidal waves are moving through a medium in the negative x-direction. Each of the waves has…

A: In the question it is given that the two waves are moving in the same negative x-direction. their…

Q: A transverse mechanical wave propagating on a string of linear density 29.2 g/m is described by the…

Q: A standing wave on a stretched string with a tension force F_T and of length L = 2 m has the…

A: We get, k=2π Also, k=2πλ 2πλ=2πλ=1 m

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

A: Equation of motion for a transverse wave Compare the given equation with the above equation

Q: Two sinusoidal waves are moving through a medium in the negative x-direction. Each of the waves has…

Q: The wave function for a standing wave on a string of linear mass density u = 0.2 kg/m, is given by…

A: The Given data is

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

Q: A standing wave with wavelength A = 1.2 m and frequency f = 50 Hz is generated %3D on a stretched…

A: Given data, Wavelength of wave, λ=1.2 m. Frequency, f=50 Hz. Max. transverse speed, vmax=2π m/s.…

Q: A standing wave on a stretched string with a tension force F_T and of length L = 2 %3D m has the…

A: A standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak…

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

A: Given:- y(x,t) =0.1sin2πx-300tμ=100 g/m Find:- The total energy on the string 22.5 J 45 J 450…

Q: The wave functions for two waves traveling on a string are described by: y(x, t) = A sin (nx-40nt)…

Q: A travelling wave on a taut string is given by the wave function: y(x,t) = 0.1 sin(2rtx - 300t),…

A: Energy associated with travelling wave E = (1/2) mw^2 A^2 A = amplitude W = angular speed m=…

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

A: Write the standard resultant wave equation due to the superimposition of the two sinusoidal waves as…

Q: A horizontal wire is stretched with a tension of 94.0 N, and the speed of transverse waves for the…

Q: A standing wave with wavelength A = 1.2 m and frequency f = 80 Hz is generated on a stretched cord.…

A: The maximum velocity is given by v = w A where, w is the angular frequency and A is the amplitude.…

Q: A wave is modeled with the function y(x,t)=4 cm cos(0.75m−1x+2.5s−1t+π/4). Find the (a)…

A: Given wave function: yx,t=4cm×cos0.75m-1x+2.5s-1t+π4 1

Q: A wave is represented by y=(3.00m)sin(2.5t-3.14x). Find (a) amplitude, (b) angular velocity, (c)…

A: According to company policy only first three subparts will be answered here. Please post the rest…

Q: A travelling wave on a taut string is given by the wave function: y(x,t) = 0.1sin(2T - 200t), where…

Q: If y(x,t) = (6.5 mm) sin[kx + (650 rad/s)t + p] describes a wave traveling along a string, how much…

A: y(x,t) = (6.5 mm) sin [kx + 650 rad/s t + ϕ] y1 = 2.9 mm ; y2 = -2.9 mm for y1 = +2.9 mm 2.9 = 6.5…

Q: The wavefunction for a wave on a taut string of linear mass densityµ = 40 g/m is given by: y(x,t) =…

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

A: Given: The equation of the transverse wave is given as. y=0.5sin4πt+5πx…

Q: A standing wave on a stretched string with a tension force F T and of length L = 2 m has the…

A: Given, Length of string L = 2 m Velocity is reduce by factor 3

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

A: Given: The wave function (y(x,t)) for the wave in a taut string is given by 0.1Sin(2πx-300t). The…

Q: A standing wave with wavelength = 1.2 m and frequency f = 80 Hz is %3D generated on a stretched…

A: Wavelength of the standing wave λ=1.2 m Frequency of the standing wave f=80 Hz Displacement of wave…

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

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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

A: 250 W

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

Q: A sinusoidal wave on a string is described by the following equation where k = 3.10 rad/cm and ω =…

A: Introduction: There are two different types of the wave, namely transverse and longitudinal wave.…

Q: Two sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase…

A: Given, Wavelength,λ=23m Amplitude,A=6 cm Wave velocity,v= 60 m/s Phase difference, ϕ=φ

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

Q: A standing wave with wavelength A = 1.2 m and frequency f = 100 Hz is generated on a stretched cord.…

A: vmax=AωA=vmaxω=vmax2πf

Q: wave functions for two waves traveling on a string are described by: y1 (x, t) = A sin (3nx- 40nt)…

A: (given) y1=A sin3πx-40πt,y2=A sin3πx+40πt By using principle of superposition, y= y1+y2 =2A…

Q: A standing wave is produced by to identical wave traveling in opposite directions. If the wave…

Q: A steel wire with mass 28.0 g and length 1.26 m is strung on a bass so that the distance from the…

Q: If y(x,t) = ( 5.6 mm) sin[kx + (460 rad/s)t + p] describes a wave traveling along a string, how much…

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

A: Given:- y(x,t) = 0.1sin4x+100t μ=0.1 kg/m Tension T is reduced by factor 2 keeping the amplitude…

Concept explainers

Interference of sound

Seiche

A seiche is an oscillating standing wave in a body of water. The term seiche pronounced saysh) can be understood by the sloshing of water back and forth in a swimming pool. The same phenomenon happens on a much larger scale in vast bodies of water including bays and lakes. A seizure can happen in any enclosed or semi-enclosed body of water.

Question

A wave traveling along a string is described by f (x, t) = a sin (abx + qt)
with a = 30.0 mm, b = 0.3 m1 and q = 10.5 s1.
Calculate
(a) (:
(b)
(c)
(d)
(e
the amplitude (in m),
the wavelength (in m),
the period (in s).
and speed of the wave (m/s).
Compute the y component of the displacement of the string (in m) at x= 0.5 m and t= 1.60 s.

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 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)
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?
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?
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?
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?
The speed of a transverse wave on a string is 300.00 m/s, its wavelength is 0.50 m, and the amplitude is 20.00 cm. How much time is required for a particle on the string to move through a distance of 5.00 km?
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?
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 ?
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 amplitude of a wave is doubled, with no other changes made to the wave. As a result of this doubling, which of the following statements is correct? (a) The speed of the wave changes. (b) The frequency of the wave changes. (c) The maximum transverse speed of an element of the medium changes. (d) Statements (a) through (c) are all true. (e) None of statements (a) through (c) is true.
A sound wave can be characterized as (a) a transverse wave, (b) a longitudinal wave, (c) a transverse wave or a longitudinal wave, depending on the nature of its source, (d) one that carries no energy, or (e) a wave that does not require a medium to be transmitted from one place to the other.
Two traveling sinusoidal waves are described by the wave functions y1 = 5.00 sin [(4.00x 1 200t)] y2 = 5.00 sin [(4.00x 1 200t 0.250)] where x, y1 and y2 are in meters and t is in seconds. (a) What is the amplitude of the resultant wave function y1 + y2? (b) What is the frequency of the resultant wave function?