Understanding Waves: Period, Frequency, and Speed of a Vibrating String

[midgey]

I have what I believe to be a simple question. I've looked in the book and lecture notes and couldn't find any help, so whatever you've got would be appreciated.

A vibrating string 50.0cm long is under a tension of 1.00 N. The results from five successive stroboscopic pictures are shown in Fig. 15.34. The strobe rate is set at 5000 flashes per minute and observations reveal that the maximum displacement occurred at flashes 1 and 5 with no other maxima in between.
a)Find the period, frequency, and wavelength for the traveling waves on this string.

I don't have a scanner, but fig 15.34 shows what looks like 5 simple sin graphs. They look like this order:

1)sin(x)
2).5sin(x)
3)sin(0)
4).5sin(-x)
5)sin(-x)

My guess for period looks like this:
5000/60 = 83.3 flashes/sec
5flashes/83.3 = .06 seconds = period

I'm pretty sure that's wrong, but its all I could come up with. If somebody helps me get the period, I can handle the rest.

b) In what normal mode (harmonic) is the string vibrating?

Since in fig 15.34 they only intersect at one point, it is operating in the second harmonic.

c) What is the speed of the traveling waves on the string

With wavelength and frequency, I can easily find this.

d) How fast is point P moving when the string is in: position 1 and position 3?

P is at the crest of the graph of sin(x). I'm pretty sure I just need to find the transversal velocity here, so that shouldn't be much of a problem. Set up the wave function and take the partial derivative w.r.t. to time.

e) What is the mass of the string?

I could use a little help on this one.

Thats it. Any and all help will be appreciated.

 

[midgey]

Actually, with a little more thought, I'm pretty sure that I need to multiply my period by 2 in order to get a full period. So my period ends up being .12 seconds. Am I right?

 

[Doc Al]

I don't have a scanner, but fig 15.34 shows what looks like 5 simple sin graphs. They look like this order:

1)sin(x)
2).5sin(x)
3)sin(0)
4).5sin(-x)
5)sin(-x)

I will assume you meant to write:
1)sin(x)
2).5sin(x)
3)0sin(x)
4)-.5sin(x)
5)-sin(x)

And how much of a sine wave is depicted? I assume (based on your later comments) from 0 to 2π radians?

My guess for period looks like this:
5000/60 = 83.3 flashes/sec
5flashes/83.3 = .06 seconds = period

First find the time between flashes: 60 sec/ 5000 flashes = 0.012 sec; so the time between flash 1 and flash 5 would be 4 x 0.012 = 0.048 sec. And, assuming I understand what you've been saying, that will be half the period, so period = 0.098 sec.

e) What is the mass of the string?

I could use a little help on this one.

Once you've found the speed (v) of the wave on the string, you need to relate that to the tension and mass of the string:
$$v = \sqrt{\frac{T}{(M/L)}}$$
Where T = tension, M/L = mass per unit length of string. You can solve for the mass.