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Characteristics of a traveling wave on a string

A transverse wave on a taut string is modeled with the wave function

y ( x , t ) = A sin ( k x w t ) = 0.2 m sin ( 6.28 m −1 x 1.57 s −1 t ) .

Find the amplitude, wavelength, period, and speed of the wave.


All these characteristics of the wave can be found from the constants included in the equation or from simple combinations of these constants.


  1. The amplitude, wave number, and angular frequency can be read directly from the wave equation:
    y ( x , t ) = A sin ( k x w t ) = 0.2 m sin ( 6.28 m −1 x 1.57 s −1 t ) .
    ( A = 0.2 m; k = 6.28 m −1 ; ω = 1.57 s −1 )
  2. The wave number can be used to find the wavelength:
    k = 2 π λ . λ = 2 π k = 2 π 6.28 m −1 = 1.0 m .
  3. The period of the wave can be found using the angular frequency:
    ω = 2 π T . T = 2 π ω = 2 π 1.57 s −1 = 4 s .
  4. The speed of the wave can be found using the wave number and the angular frequency. The direction of the wave can be determined by considering the sign of k x ω t : A negative sign suggests that the wave is moving in the positive x -direction:
    | v | = ω k = 1.57 s −1 6.28 m −1 = 0.25 m/s .


All of the characteristics of the wave are contained in the wave function. Note that the wave speed is the speed of the wave in the direction parallel to the motion of the wave. Plotting the height of the medium y versus the position x for two times t = 0.00 s and t = 0.80 s can provide a graphical visualization of the wave ( [link] ).

Figure shows two transverse waves whose y values vary from -0.2 m to 0.2 m. One wave, marked t=0 seconds is shown as a dotted line. It has crests at x equal to 0.25 m and 1.25 m. The other wave, marked t=0.8 seconds is shown as a solid line. It has crests at x equal to 0.45 m and 1.45 m.
A graph of height of the wave y as a function of position x for snapshots of the wave at two times. The dotted line represents the wave at time t = 0.00 s and the solid line represents the wave at t = 0.80 s . Since the wave velocity is constant, the distance the wave travels is the wave velocity times the time interval. The black dots indicate the points used to measure the displacement of the wave. The medium moves up and down, whereas the wave moves to the right.

There is a second velocity to the motion. In this example, the wave is transverse, moving horizontally as the medium oscillates up and down perpendicular to the direction of motion. The graph in [link] shows the motion of the medium at point x = 0.60 m as a function of time. Notice that the medium of the wave oscillates up and down between y = + 0.20 m and y = −0.20 m every period of 4.0 seconds.

Figure shows a transverse wave on a graph. Its y value varies from -0.2 m to 0.2 m. The x axis shows the time in seconds. The horizontal distance between two identical parts of the wave is labeled T = 4 seconds.
A graph of height of the wave y as a function of time t for the position x = 0.6 m . The medium oscillates between y = + 0.20 m and y = −0.20 m every period. The period represented picks two convenient points in the oscillations to measure the period. The period can be measured between any two adjacent points with the same amplitude and the same velocity, ( y / t ) . The velocity can be found by looking at the slope tangent to the point on a y -versus- t plot. Notice that at times t = 3.00 s and t = 7.00 s , the heights and the velocities are the same and the period of the oscillation is 4.00 s.

Check Your Understanding The wave function above is derived using a sine function. Can a cosine function be used instead?

Yes, a cosine function is equal to a sine function with a phase shift, and either function can be used in a wave function. Which function is more convenient to use depends on the initial conditions. In [link] , the wave has an initial height of y ( 0.00 , 0.00 ) = 0 and then the wave height increases to the maximum height at the crest. If the initial height at the initial time was equal to the amplitude of the wave y ( 0.00 , 0.00 ) = + A , then it might be more convenient to model the wave with a cosine function.

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Questions & Answers

what is the value of x 6yx7y
Elijah Reply
what is the formula for frictional force
bassey Reply
I believe, correct me if I am wrong, but Ffr=Fn*mu
frictional force ,mathematically Fforce (Ffr) =K∆R where by K stands for coefficient of friction ,R stands for normal force/reaction NB: R = mass of a body ( m) x Acc.due gravity (g) The formula will hold the meaning if and only if the body is relatively moving with zero angle (∅ = 0°C)
What is concept associated with linear motion
Adeoye Reply
what causes friction?
uneven surfaces cause friction Elijah
rough surfacea
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shane Reply
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What is motion
Adeoye Reply
moving place to place
change position with respect to surrounding
to which
to where ?
the phenomenon of an object to changes its position with respect to the reference point with passage of time then it is called as motion
it's just a change in position
reference point -it is a fixed point respect to which can say that a object is at rest or motion
A change in position
change in position depending on time
Is there any calculation for line integral in scalar feild?
Sadia Reply
yes I'm available
what is thrust
Aarti Reply
when an object is immersed in liquid, it experiences an upward force which is called as upthrust.
@Phanindra Thapa No, that is buoyancy that you're talking about...
thrust is simply a push
it is a force that is exerted by liquid.
what is the difference between upthrust and buoyancy?
The force exerted by a liquid is called buoyancy. not thrust. there are many different types of thrust and I think you should Google it instead of asking here.
hey Kumar, don't discourage somebody like that. I think this conversation is all about discussion...remember that the more we discuss the more we know...
thrust is an upward force acting on an object immersed in a liquid.
uptrust and buoyancy are the same
the question isn't asking about up thrust. he simply asked what is thrust
a Thrust is simply a push
the perpendicular force applied on the body
thrust is a force of depression while
what is friction?
while upthrust is a force that act on a body when it is fully or partially submerged in a liquid
mathematically upthrust (u) = Real weight (wr) - Apparent weight (wa) u = wr- wa.
friction is a force which opposes relative motion.
how did astromers neasure the mass of earth and sun
papillas Reply
wats the simplest and shortest formula to calc. for order of magnitude
Distinguish between steamline and turbulent flow with at least one example of each
Aarti Reply
what is newtons first law
Theodore Reply
It state that an object in rest will continue to remain in rest or an object in motion will continue to remain in motion except resultant(unbalanced force) force act on it
Thanks Gerald Fokumla
Your welcome
it states that a body remains in its state of rest or uniform motion unless acted upon by resultant external force.
it that a body continues to be in a state of rest or in straight line in a motion unless there is an external force acting on it
state's that a body will continue to maintain it present state of or of uniform unless it's being called upon by an external force
derive the relation above
jeba Reply
formula for find angular velocity
Mark Reply
Why satellites don't fall on earth? Reason?
Abdur Reply
because space doesn't have gravity
satellites technically fall to earth but they travel parallel to earth so fast that they orbit instead if falling(plus the gravity is also weaker in the orbit). its a circular motion where the centripetal force is the weight due to gravity
Exactly everyone what is gravity?
Tebogo Reply
the force that attrats a body towards the center of earth,or towards any other physical body having mass
That force which attracts or pulls two objects to each other. A body having mass has gravitational pull. If the object is bigger in mass then it's gravitational pull would be stronger.For Example earth have gravitational pull on other objects that is why we are pulled by earth.
Gravity is the force that act on a on body to the center of the earth.
gravity is a force of Attraction
Qn1(a) Why during the day sky seen blue colour? (b)why during the sunset its seen reddish colour ?
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Sana Reply
It's applicable when determining the amount of force needed to make a body to move or to stop a moving body
Practice Key Terms 4

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