<< Chapter < Page Chapter >> Page >

If you shake the end of a stretched spring up and down with a frequency f , you can produce a sinusoidal, transverse wave propagating down the spring. Does the wave number depend on the frequency you are shaking the spring?

The wavelength is equal to the velocity of the wave times the frequency and the wave number is equal to k = 2 π λ , so yes, the wave number will depend on the frequency and also depend on the velocity of the wave propagating through the spring.

Got questions? Get instant answers now!

Does the vertical speed of a segment of a horizontal taut string through which a sinusoidal, transverse wave is propagating depend on the wave speed of the transverse wave?

Got questions? Get instant answers now!

In this section, we have considered waves that move at a constant wave speed. Does the medium accelerate?

The medium moves in simple harmonic motion as the wave propagates through the medium, continuously changing speed, therefore it accelerates. The acceleration of the medium is due to the restoring force of the medium, which acts in the opposite direction of the displacement.

Got questions? Get instant answers now!

If you drop a pebble in a pond you may notice that several concentric ripples are produced, not just a single ripple. Why do you think that is?

Got questions? Get instant answers now!

Problems

A pulse can be described as a single wave disturbance that moves through a medium. Consider a pulse that is defined at time t = 0.00 s by the equation y ( x ) = 6.00 m 3 x 2 + 2.00 m 2 centered around x = 0.00 m . The pulse moves with a velocity of v = 3.00 m/s in the positive x -direction. (a) What is the amplitude of the pulse? (b) What is the equation of the pulse as a function of position and time? (c) Where is the pulse centered at time t = 5.00 s ?

Got questions? Get instant answers now!

A transverse wave on a string is modeled with the wave function y ( x , t ) = ( 0.20 cm ) sin ( 2.00 m −1 x 3.00 s −1 t + π 16 ) . What is the height of the string with respect to the equilibrium position at a position x = 4.00 m and a time t = 10.00 s ?

y ( x , t ) = −0.037 cm

Got questions? Get instant answers now!

Consider the wave function y ( x , t ) = ( 3.00 cm ) sin ( 0.4 m −1 x + 2.00 s −1 t + π 10 ) . What are the period, wavelength, speed, and initial phase shift of the wave modeled by the wave function?

Got questions? Get instant answers now!

A pulse is defined as y ( x , t ) = e −2.77 ( 2.00 ( x 2.00 m/s ( t ) ) 5.00 m ) 2 . Use a spreadsheet, or other computer program, to plot the pulse as the height of medium y as a function of position x . Plot the pulse at times t = 0.00 s and t = 3.00 s on the same graph. Where is the pulse centered at time t = 3.00 s ? Use your spreadsheet to check your answer.

Figure shows two pulse waves. Both have y values varying from 0 to 1. The first wave, shown as a dotted line is marked t=0 seconds. The crest of the wave is at x=0. The second wave, shown as a solid line is marked t= 3 seconds. The crest of the wave is at x=6.
The pulse will move Δ x = 6.00 m .

Got questions? Get instant answers now!

A wave is modeled at time t = 0.00 s with a wave function that depends on position. The equation is y ( x ) = ( 0.30 m ) sin ( 6.28 m −1 x ) . The wave travels a distance of 4.00 meters in 0.50 s in the positive x -direction. Write an equation for the wave as a function of position and time.

Got questions? Get instant answers now!

A wave is modeled with the function y ( x , t ) = ( 0.25 m ) cos ( 0.30 m −1 x 0.90 s −1 t + π 3 ) . Find the (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) phase shift, (f) wavelength, and (g) period of the wave.

a. A = 0.25 m ; b. k = 0.30 m −1 ; c. ω = 0.90 s −1 ; d. v = 3.0 m/s ; e. ϕ = π / 3 rad ; f. λ = 20.93 m ; g. T = 6.98 s

Got questions? Get instant answers now!

A surface ocean wave has an amplitude of 0.60 m and the distance from trough to trough is 8.00 m. It moves at a constant wave speed of 1.50 m/s propagating in the positive x -direction. At t = 0 , the water displacement at x = 0 is zero, and v y is positive. (a) Assuming the wave can be modeled as a sine wave, write a wave function to model the wave. (b) Use a spreadsheet to plot the wave function at times t = 0.00 s and t = 2.00 s on the same graph. Verify that the wave moves 3.00 m in those 2.00 s.

Got questions? Get instant answers now!

A wave is modeled by the wave function y ( x , t ) = ( 0.30 m ) sin [ 2 π 4.50 m ( x 18.00 m s t ) ] . What are the amplitude, wavelength, wave speed, period, and frequency of the wave?

A = 0.30 m , λ = 4.50 m , v = 18.00 m/s , f = 4.00 Hz , T = 0.25 s

Got questions? Get instant answers now!

A transverse wave on a string is described with the wave function y ( x , t ) = ( 0.50 cm ) sin ( 1.57 m −1 x 6.28 s −1 t ) . (a) What is the wave velocity of the wave? (b) What is the magnitude of the maximum velocity of the string perpendicular to the direction of the motion?

Got questions? Get instant answers now!

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.

y ( x , t ) = 0.23 m sin ( 3.49 m −1 x 0.63 s −1 t )

Got questions? Get instant answers now!

Consider a wave described by the wave function y ( x , t ) = 0.3 m sin ( 2.00 m −1 x 628.00 s −1 t ) . (a) How many crests pass by an observer at a fixed location in 2.00 minutes? (b) How far has the wave traveled in that time?

Got questions? Get instant answers now!

Consider two waves defined by the wave functions y 1 ( x , t ) = 0.50 m sin ( 2 π 3.00 m x + 2 π 4.00 s t ) and y 2 ( x , t ) = 0.50 m sin ( 2 π 6.00 m x 2 π 4.00 s t ) . What are the similarities and differences between the two waves?

They have the same angular frequency, frequency, and period. They are traveling in opposite directions and y 2 ( x , t ) has twice the wavelength as y 1 ( x , t ) and is moving at half the wave speed.

Got questions? Get instant answers now!

Consider two waves defined by the wave functions y 1 ( x , t ) = 0.20 m sin ( 2 π 6.00 m x 2 π 4.00 s t ) and y 2 ( x , t ) = 0.20 m cos ( 2 π 6.00 m x 2 π 4.00 s t ) . What are the similarities and differences between the two waves?

Got questions? Get instant answers now!

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?

Each particle of the medium moves a distance of 4 A each period. The period can be found by dividing the velocity by the wavelength: t = 10.42 s

Got questions? Get instant answers now!

Questions & Answers

Suppose the master cylinder in a hydraulic system is at a greater height than the cylinder it is controlling. Explain how this will affect the force produced at the cylinder that is being controlled.
Louise Reply
Why is popo less than atmospheric? Why is popo greater than pipi?
Louise
The old rubber boot shown below has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of Leak 1? Explain your responses in terms of energy.
Louise
David rolled down the window on his car while driving on the freeway. An empty plastic bag on the floor promptly flew out the window. Explain why.
Louise Reply
the pressure differential exerted a force on the bag greater than the gravitational force holding it on the floor.
gtitboi
what is angular velocity
Sthandazile Reply
The rate of change in angular displacement is defined as angular velocity.
Manorama
a length of copper wire was measured to be 50m with an uncertainty of 1cm, the thickness of the wire was measured to be 1mm with an uncertainty of 0.01mm, using a micrometer screw gauge, calculate the of copper wire used
Nicole Reply
What is the answer please
Mustapha
If centripetal force is directed towards the center,why do you feel that you're thrown away from the center as a car goes around a curve? Explain
Maira Reply
if there is a centripetal force it means that there's also a centripetal acceleration, getting back to your question, just imagine what happens if you pull out of a car when it's quickly moving or when you try to stop when you are running fast, anyway, we notice that there's always a certain force..
Lindomar
... that tends to fight for its previous direction when you try to attribute to it an opposite one ou try to stop it.The same thing also happens whe a car goes around a curve, the car it self is designed to a"straight line"(look at the position of its tyres, mainly the back side ones), so...
Lindomar
... whenever it goes around a curve, it tends to throw away its the occupiers, it's given to the fact that it must interrupt its initial direction and take a new one.
Lindomar
Which kind of wave does wind form
Matthias Reply
calculate the distance you will travel if you mantain an average speed of 10N m/s for 40 second
Abdulai Reply
400m/s
Feng
hw to calculate the momentum of the 2000.0 elephant change hunter at a speed of 7.50 m/s
Kingsley Reply
how many cm makes 1 inches
Hassan Reply
2.5
omwoyo
2.54cm=1inche
omwoyo
how do we convert from m/s to km/hr
Toni Reply
When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why?
SANA Reply
Explain why polarization does not occur in sound
Nuradeen
one ship sailing east with a speed of 7.5m/s passes a certain point at 8am and a second ship sailing north at the same speed passed the same point at 9.30am at what distance are they closet together and what is the distance between them then
Kuber Reply
density of a subtance is given as 360g/cm,put it in it s.i unit form
Linda Reply
if m2 is twice of m1. find the ration of kinetic energy in COM system to lab system of elastic collision
Raman Reply
What is a volt equal to?
Clifton Reply
Practice Key Terms 4

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 1' conversation and receive update notifications?

Ask