Two transverse sinusoidal waves combining in a string are described by the wavefunctions y1 = 0.02 sin(4ttx+tt) and y2 = 0.02 sin(4ttx-tt), where x and y are inmeters, and t is in seconds. If after superposition, a standing wave of 3 loops isformed, then the length of the string is:%3DO 2 mO 1.5 mO 0.5 m0.75 m1 mA=6 cm and Clear selectionA standing wave on a stretched string with a tension force F_T and of length L = 2m has the following equation: y(x,t) = 0.1 sin(2Ttx) cos(100rt). How many loopswould appear on the string if the velocity is reduced by a factor of 3 while thefrequency is held constant?3 loopsO 6 loopsO 12 loopsO 2 loops4 loops

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

Two transverse sinusoidal waves combining in a string are described by the wave functions y1 = 0.02 sin(4ttx+tt) and y2 = 0.02 sin(4ttx-tt), where x and y are in %3D %3D meters, and t is in seconds. If after superposition, a standing wave of 3 loops is formed, then the length of the string is:

Two transverse sinusoidal waves combining in a string are described by the wave functions y1 = 0.02 sin(4ttx+tt) and y2 = 0.02 sin(4ttx-tt), where x and y are in %3D %3D meters, and t is in seconds. If after superposition, a standing wave of 3 loops is formed, then the length of the string is:

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter18: Superposition And Standing Waves

Section: Chapter Questions

Problem 18.55P

See similar textbooks

Related questions

Q: Two sinusoidal waves with the same amplitude of 9.03 mm and the same wavelength travel together…

Q: A standing wave on a stretched string fixed at both ends is described by: y(x,t) = 0.1 %3D sin(2Ttx)…

A: Given data: yx,t=0.1sin2πxcos100πt Length of the string, L=1 m At, t = 0, x = 0.75 m

Q: Consider two sinusoidal waves traveling along a string, modeled as y1 (x, y) = 0.2 m sin(4…

Q: A standing wave on a string of length L = 3 m is described by the following equation: y(x.t) - 0.08…

A: Given, Length of string,L=3 m Equation of standing wave,y=0.08sin(2πx)cos(300πt)

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

A: Let A, k, x, ω, and t denote the amplitude of the sinusoidal wave, propagation constant, position,…

Q: A standing wave on a string of length L = 3 m is described by the following equation: y(x,t) = 0.08…

A: Given equation is, y(x,t)=0.08 sin (2πx) cos (300 πt) On compare this equation with y = A…

Q: A transverse periodic wave on a string with a linear density of 0.26 kg/m is described by the…

A: Given that the transverse periodic wave equation and linear density of the string.Then We have to…

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(xt)-…

Q: Consider two sinusoidal sine waves traveling along a string, modeled as y1 (x, t) = 0.3 m sin (4 m−1…

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

Q: Two identical sinusoidal waves with wavelengths of 1.5 m travel in the same direction at a speed of…

A: Wavelength of each wave λ=1.5 m Speed of each wave v=25 m/s Amplitude of the resultant wave R=3A

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

A: We are allowed to answer only the first question. For solutions to other questions, please re-post…

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

A: Both the superposing waves are opposing each other Hence, the resultant wave due to the…

Q: The following two waves are sent in opposite directi y1(x, t) = (8.60 mm) sin(4.607x - 400at) y2(x,…

Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2Ttx) cos(50t), where x…

A: Shortest distance between node and antinode is (1/4) of wavelength.

Q: A standing wave on a string of length L = 3 m is described by the following equation: y(x,t) = 0.08…

A: Length of string: L = 3 m Equation of standing wave: y(x,t) = 0.08sin(2πx)cos(300πt)

Q: A standing wave has the following wave- function: y(x,t) = 0.2 sin(Ttx) cos(12Tt), where x and y are…

A: Given data: Wave equation: yx,t=0.2 sinπxcos12πt Length of the string, L=2 m

Q: A sinusoidal wave travelling in the positive x-direction has a wavelength of 0.4 m, an amplitude of…

Q: The function y(x, t) = (22.0 cm) cos(πx - 23πt), with x in meters and t in seconds, describes a wave…

A: The wave y(x,t) = 22 Cos (πx - 23πt)

Q: A standing wave on string of length L = 3 m is described by the following equation 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: The maximum velocity is given by v = w A where, w is the angular frequency and A is the amplitude.…

Q: If a standing wave on a string is produced by the superposition of th following two waves: y1= A…

A: From the principle of superposition we can write the total displacement of the string is…

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

Q: Consider two sinusoidal waves traveling along a string, modeled as y1 (x, t) = 0.3 m sin (4 m−1 x +…

A: When two waves y1 and y2 interfere with each other, then according to principle of superposition the…

Q: Two sinusoidal waves with the same amplitude of 9.03 mm and the same wavelength travel together…

A: Amplitude, ym = 9.03 mm Equation of wave, y(x, t) = ymsin(kx ± ωt + Φ1) H = 8.1 mm

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

A: Given Data: Wavelength, λ=1.2 m Frequency, f=50 Hz Element position, x=0.5 m Max. velocity at x=0.5…

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

A: f= v2L = 12LTμ v= ωk ω= 100π(from the wave equation) Tμ = ωk2 T = 100π2π2x 0.01 = 25 N

Q: The equation of a standing wave is y(x,t) = 0.8 cos(0.2Ttx) sin(200rt) %3D where x and y are in cm…

A: The distance between the two successive nodes is, L=λ2 The wavelength of the wave is,…

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

A: Given, Wavelength λ=1.2 m Frequency f = 50 Hz x = 0.5 m Minimum transverse velocity v = 2π m/s

Q: The following two waves are sent in opposite directionson a horizontal string so as to create a…

A: The time period is,

Q: A sinusoidal wave travelling in the positive x-direction has a wavelength of 0.4 m, an amplitude of…

Q: A sinusoidal wave traveling in the positive x direction has a wavelength of 0.5m , an amplitude of…

A: The general equation of a sinusoidal wave is given by: Where φ is the phase. Substitute the values…

Q: A standing wave has the following wave-function: y(x,t) = 0.2 sin(TtX) cos(12rt), where x and y are…

A: Length, L=2 m

Q: A standing wave with wavelength A = 1.2 m and frequency f = 100 Hz is generated %3D on a stretched…

A: wave velocity = frequency x wavelength maximum velocity = w A where, w is the angular frequency…

Q: A standing wave with wavelength of 2 m, speed of 20 m/s and amplitude of 8 mm is generated on a taut…

A: Standing waves: When two progressive waves of same amplitude , time period, and same speed are…

Q: A standing wave has the following wave- function: y(x,t) = 0.2 sin(3ttx) cos(12Ttt), where x and y…

A: given , standing wave , y(x,t) = 0.2 sin(3πx) cos(12πt) .............(1) length of the string , L =…

Q: A standing wave on a string is described by the wave function y(x,t) = (6 mm) sin(4Ttx)cos(30tt).…

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: A standing transverse wave is generated in a string clamped at its both ends whose equation is given…

A: Given, Equation of wave, y=6sin(2π3x)cos(120πt)

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: A standing wave on a string of length L = 3 m is described by the following equation: y(x,t) = 0.08…

Q: Two sinusoidal waves with the same amplitude of 9.03 mm and the same wavelength travel together…

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

Q: A standing wave has the following wave-function: y(x,t) = 0.2 sin(3rtx) cos(12rtt),. where x and y…

A: Length, L= 2m Comparing given equation with standard equation, y=Asin(kx)cos(ωt) We get, k=3π

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

Two transverse sinusoidal waves combining in a string are described by the wave
functions y1 = 0.02 sin(4ttx+tt) and y2 = 0.02 sin(4ttx-tt), where x and y are in
meters, and t is in seconds. If after superposition, a standing wave of 3 loops is
formed, then the length of the string is:
%3D
O 2 m
O 1.5 m
O 0.5 m
0.75 m
1 m
A=6 cm and

Clear selection
A standing wave on a stretched string with a tension force F_T and of length L = 2
m has the following equation: y(x,t) = 0.1 sin(2Ttx) cos(100rt). How many loops
would appear on the string if the velocity is reduced by a factor of 3 while the
frequency is held constant?
3 loops
O 6 loops
O 12 loops
O 2 loops
4 loops

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

Step 2

Step 3

Step 4

Step by step

Solved in 4 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

A trough with dimensions 10.00 meters by 0.10 meters by 0.10 meters is partially filled with water. Smallamplitude surface water waves are produced from both ends of the trough by paddles oscillating in simple harmonic motion. The height of the water waves are modeled with two sinusoidal wave equations, y1(x,t)=0.3msin(4m1x3s1t) and y2(x,t)=0.3mcos(4m1x+3s1t2) . What is the wave function of the resulting wave after the waves reach one another and before they reach the end of the trough (i.e., assume that there are only two waves in the trough and ignore reflections)? Use a spreadsheet to check your results. (Hint: Use the trig identities sin(uv)=sinucosvcosusinv and sin(uv)=sinucosvcosusinv
Two transverse waves travel through a taut string. The speed of each wave is v=30.00 m/s. A plot of the vertical position as a function of the horizontal position is shown below for the time t=0.00 s. (a) What is the wavelength of each wave? (b) What is the frequency of each wave? (c) What is the maximum vertical speed of each string?
(a) Students in a physics lab are asked to find the length of an air column in a tube closed at one end that has a fundamental frequency of 256 Hz. They hold the tube vertically and fill it with water to the top, then lower the water while a 256—Hz tuning fork is rung and listen for the first resonance. What is the air temperature if the resonance occurs for a length of 0.336 m? (b) At what length will they observe the second resonance (first overtone)?
A swimmer in the ocean observes one day that the ocean surface waves are periodic and resemble a sine wave. The swimmer estimates that the vertical distance between the crest and the trough of each wave is approximately 0.45 m, and the distance between each crest is approximately 1.8 m. The swimmer counts that 12 waves pass every two minutes. Determine the simple harmonic wave function that would describes these waves.
A string on the violin has a length of 24.00 cm and a mass of 0.860 g. The fundamental frequency of the string is 1.00 kHz. (a) What is the speed of the wave on the string? (b) What is the tension in the string?
A wave traveling on a Slinky® mat is stretched to 4 m takes 2.4 s to travel the length at me Slinky and back again. (a) What is the speed of the wave? (b) Using the same Slinky stretched to the same length, a standing wave is created which consists of three antinodes and four nodes. At what frequency must the Slinky be oscillating?
Why is a pulse on a string considered to be transverse?
On a marimba (Fig. P18.75), the wooden bar that sounds a tone when struck vibrates in a transverse standing wave having three ant modes and two nodes. The lowest-frequency note is 87.0 Hz, produced by a bar 40.0 cm long, (a) Find the speed of transverse waves on the bar. (b) A resonant pipe suspended vertically below the center of the bar enhances the loudness of the emitted sound. If the pipe is open at the top end only, what length of the pipe is required to resonate with the bar in part (a)?
Sine waves are sent down a 1.5-m-long string fixed at both ends. The waves reflect back in the opposite direction. The amplitude of the wave is 4.00 cm. The propagation velocity of the waves is 175 m/s. The n=6 resonance mode of the string is produced. Write an equation for the resulting standing wave.
Check Your Understanding The wave equation 2y(x,t)x2=1v22y(x,t)t2 works for any wave of the form y(x,t)=f(xvt) . In the previous section, we stated that a cosine function could also be used to model a simple harmonic mechanical wave. Check if the wave y(x,t)=0.50mcos(0.20m1x4.00s1t+10) is a solution to the wave equation. Any disturbance that complies with the wave equation can propagate as a wave moving along the x-axis with a wave speed v. It works equally well for waves on a string, sound waves, and electromagnetic waves. This equation is extremely useful. For example, it can be used to show that electromagnetic waves move at the speed of light.
A string of a constant linear mass density is held taut by two students, each holding one end. The tension in the string is constant. The students each send waves down the string by wiggling the string. (a) Is it possible for the waves to have different wave speeds? (b) Is it possible for the waves to have different frequencies? (c) Is it possible for the waves to have different wavelengths?
In an earthquake, both S (transverse) and P (longitudinal) waves propagate from the focus of the earthquake. The focus is in the ground radially below the epicenter on the surface (Fig. (CQ16.9). Assume the waves move in straight lines through uniform material. The S waves travel through the Earth more slowly than the P waves (at about 5 km/s versus 8 km/s). By detecting the time of arrival of the waves at a seismograph. (a) how can one determine the distance to the focus of the earthquake? (b) How many detection stations are necessary to locate the focus unambiguously?