What is the distance traveled by a blue spot on a transverse wave in one period?

[FlipStyle1308]

A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 1.4 s, and the wave travels along the string at 0.6 m/s. The amplitude of the wave is 0.1 m. The frequency at which the crests pass a given point in space is 0.7143 Hz. The distance between two adjacent crests on the wave is 0.84 m.

a. There is a blue spot drawn onto the rope with a magic marker. Find the distance thsi spot travels in one period.

b. If the mass per unit length of the string is 6 x 10-4 kg/m, what is the tension in the string?

For part a, I tried velocity/time, using both 0.6 and 0.84 as my answers, and both were wrong. I have a feeling part b depends on part a, so I will wait off on part b.

 

[berkeman]

The amplitude of the wave is given as part of the problem statement. What does the amplitude of the wave represent? Careful of the factor of 2x, BTW.

 

[FlipStyle1308]

Does amplitude represent the wavelength?

 

[berkeman]

Does amplitude represent the wavelength?

No, definitely not. Your textbook or other study materials should explain what the amplitude, frequency, period, wavelength, etc. are for a wave. The simplest wave on a string would be a sinusoidal traveling wave. The equation representing a single point on the string should look like this:

y(t) = A sin(wt)

Can you check your study materials, and then tell me what A and w represent in this equation?

 

[Doc Al]

No. Amplitude and wavelength are independent characteristics of a wave. (In this case they are perpendicular.)

 

[FlipStyle1308]

y(t) = 0.1 sin(0.84t) ?

 

[berkeman]

y(t) = 0.1 sin(0.84t) ?

You got the amplitude part correct (A = 0.1m), but w (omega) is not the wavelength. Omega is the angular frequency -- a sine wave oscillates through 2Pi radians every period. You are told that the frequency is one cycle every 0.7143 seconds. Does your text show you how to arrange the angular frequency and time in the argument to the sin() function?

 

[berkeman]

I googled sine wave oscillation string tutorial, and got some good hits. This is the second one, and I think it will help you:

http://www2.kutl.kyushu-u.ac.jp/seminar/MicroWorld2_E/2Part1_E/2P12_E/wave_E.htm

 

[FlipStyle1308]

Honestly, I couldn't even find the equation you gave me in the book, or at least in the chapter everything else is in!

 

[FlipStyle1308]

Hmm...so would it be y(t) = 0.1 sin(2 x pi x 0.7143) = 7.83 x 10-3 ?

 

[Doc Al]

Rather than get hung up trying to understand that sine wave equation, try answering part a by thinking what that piece of rope (the blue spot) is doing. How is it moving? How far does it move? (You do need to understand amplitude and period. That must be in your book.)

 

[FlipStyle1308]

Okay I just read over that part, but don't understand how to incorporate what I read into this problem.

 

[berkeman]

You forgot to multiply by time in the argument to the sin() function, but otherwise you got it correct for the vertical movement versus time for a single spot on the string:

y(t) = 0.1 sin (2 \pi ft)

where:
A = 0.1m
f = frequency = \frac{\omega}{2\pi} = 0.7143Hz

Now for part b, you are going to need to use the full wave equation for traveling waves on a string. For part a you only needed to think about how a single point moves up and down sinusoidally with time. The propagation of a wave down a string involves how much tension there is in the string and the mass density of the string, as well as the other stuff from part a.


EDIT -- Note that the A number is the displacement from zero up to maximum. What is then the overall peak-to-peak amplitude of the displacement?

 

[FlipStyle1308]

You forgot to multiply by time in the argument to the sin() function, but otherwise you got it correct for the vertical movement versus time for a single spot on the string:

y(t) = 0.1 sin (2 \pi ft)

where:
A = 0.1m
f = frequency = frac{\omega}{2\pi} = 0.7143Hz

Now for part b, you are going to need to use the full wave equation for traveling waves on a string. For part a you only needed to think about how a single point moves up and down sinusoidally with time. The propagation of a wave down a string involves how much tension there is in the string and the mass density of the string, as well as the other stuff from part a.

So for part a, I multiply what I got by 1.4s?

 

[berkeman]

Um no. Also note the edits that I just did to my previous post. What does vertical amplitude mean?

 

[FlipStyle1308]

Vertical amplitude is the distance up, so the total distance for one oscillation is 0.4 m?