The displacement, y , of particles in a wave travelling along the x-axis is given by y(x, t) = 2xe-x-3t + 6tex-3t for x and y measured in centimetres and t in seconds. (a) Use the one-dimensional wave equation to determine the phase speed of the wave. In what direction does the wave propagate? (b) Show that a particle at any position x along the wave obeys the equation of motion, a?y ду +6- + 9y = 0 at? at What kind of oscillation does this describe?

The displacement, y , of particles in a wave travelling along the x-axis is given by y(x, t) = 2xe-x-3t + 6tex-3t for x and y measured in centimetres and t in seconds. (a) Use the one-dimensional wave equation to determine the phase speed of the wave. In what direction does the wave propagate? (b) Show that a particle at any position x along the wave obeys the equation of motion, a?y ду +6- + 9y = 0 at? at What kind of oscillation does this describe?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter17: Sound

Section: Chapter Questions

Problem 38P: Porpoises emit sound waves that they use for navigation. If the wavelength of the sound wave emitted...

See similar textbooks

Related questions

Q: Imagine a wave traveling is stretched to total length of 3.4m and takes 2.9s to travel the length…

Q: Calculate the wave speed.

A: The velocity of a transverse wave of wavelength λ and frequency f is given by v=λf

Q: he displacement of a traveling wave as a function of position and time is given by; y(x,t) = 0.18…

A: The displacement of a travelling wave is given by

Q: 5.81 cm

A: The distance between the trough and the crest along the y-axis is B=5.81 cm distance between a…

Q: A sinusoidal wave is described by the wave function y = 1.8 sin ( 0.49 x + 28 t) where x and y are…

Q: A wave on a string is described by the wave function y = 0.100 sin(0.30x − 18t),where x and y are in…

A: (a) The given wave function of the string is, y=Asinky-ωt=0.1 msin0.30 rad/m2.40 m-18 rad/st=0.1…

Q: Which quantities determine the speed of a particle in a medium through which a wave propagates:…

A: (c) amplitude and frequency

Q: The displacement, L of particles in a wave travelling along the x-axis is given by, y(x,t) =…

A: The displacement y of the wave is, y(x, t)=2xe-x-3t + 6te-x-3t (1) The wave equation…

Q: The displacement of a traveling wave as a function of position and time is given by; y(x,t) = 0.16…

Q: the period of oscillation of a given wave is 3.4 seconds and the wave is travelling at 12 m/s, what…

A: Speed v = 12 m/s Time t = 3.4 sec

Q: A wave described by the equation (see image), where x and y are in meters and t is in seconds, is…

A: Given:- A wave described by the equation raveling down a cable has a mass per unit length of 0.41…

Q: Find (a) the amplitude, (b) the wavelength, (c) the period, and (d) the speed of a wave whose…

A: The given wave is :- y=1.0 cos( 0.75x + 33 t ) We know that the generalised equation of wave is…

Q: A transverse wave on a rope is given by- y(x,t) = 0.1m cos((0.2cm^-1)x + (20s^-1)t) (a) Find the…

A: Note:“Since you have posted a question with multiple sub-parts, we willprovide the solution only to…

Q: between x1 = 4 cm %3D che form of, y = A II

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

Q: Transverse waves on a string have a wave speed of 8.00 m / s, an amplitude of 0.070 m and a…

A: (a) The frequency of the wave can be obtained as; f=vλf=8.00 m/s0.320 m f=25.0 Hz

Q: A sinusoidal wave travels along a string. The time for a particular point to move from maximum…

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

The displacement, y , of particles in a wave travelling along the x-axis is
given by
y(x, t) = 2xe-*-3t + 6te-x-3t
for x and y measured in centimetres and t in seconds.
(a) Use the one-dimensional wave equation to determine the phase speed of the wave. In
what direction does the wave propagate?
(b) Show that a particle at any position x along the wave obeys the equation of motion,
a²y
ду
at?
+6.
+ 9y = 0
at
What kind of oscillation does this describe?

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

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

The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound intensity level goes up by 40.0 dB?
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?
How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 40.0 m and a propagation speed of 5.00 m/s?
The energy of a ripple on a pond is proportional to the amplitude squared. If the amplitude of the ripple is 0.1 cm at a distance from the source of 6.00 meters, what was the amplitude at a distance of 2.00 meters from the source?
To increase the intensity of a wave by a factor of 50, by what factor should the amplitude be increased?
What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at a wave speed of 0.800 m/s?
A bat sends of a sound wave 100 kHz and the sound waves travel through air at a speed of v=343 m/s. (a) If the maximum pressure difference is 1.30 Pa, what is a wave function that would model the sound wave, assuming the wave is sinusoidal? (Assume the phase shift is zero.) (b) What are the period and wavelength of the sound wave?
Give one example of a transverse wave and one example of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.
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 ?
Check Your Understanding Describe how amplitude is related to the loudness of a sound.
A piano wire has a linear mass density of =4.95103 kg/m. Under what tension must the string be kept to produce waves with a wave speed of 500.00 m/s?
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)