# The physics of wave properties on a string

1. Oct 26, 2009

### amandine

1. The problem statement, all variables and given/known data
The speed of a transverse wave on a string is 450 m/s, while the wavelength is 0.18 m. The amplitude of the wave is 2.0 mm.

a. What is the total up and down distance moved by the wave particle for each cycle of the wave?
b. What is the frequency of the wave?
c. What is the period of motion of the wave?
d. How many cycles of the wave would have to pass by a given point so that a particle on the string moves a total distance of 1.0 km?
e. How much time is required for a particle on a string to move through a total distance of 1.0 km?

2. Relevant equations
v = f lambra
t = 1/f
time = d/v

3. The attempt at a solution

a. Amplitude is 2.0 mm therefore the crest and trough is 4.0 mm. Up and down distance is 8.0 mm because two crest and troughs (4.0 mm) add up to 8.0 mm.

b. v = f lambra
450 m/s = f 0.18 m
450 m/s / 0.18 m = f
f = 2500 Hz

c. t = 1/f
t = 1 / 2500 Hz
t = 0.0004 s

d. 1 km = 1,000 m but this is it because I don't know what to do.

e. time = d/v
time = 1000 m/450 m/s
time = 2.22 s

I think my answers are right but correct me if I'm wrong.

2. Oct 26, 2009

### Delphi51

You can't do e until you get d. Others look good!
For d, remember that the particles of the string only move transversely (side to side) so you have 4 mm out to the crest, 4 mm back to center, ... and so on. Figure out the total distance moved in one cycle (which is one period or one wavelength). Then it will be easy to get the number of such cycles that gives 1 km of distance moved side to side.

3. Oct 26, 2009

### amandine

The 8 mm must be in m if I'm doing this: 0.18/8 or 0.008 = 0.0225 or 22.5

4. Oct 26, 2009

### Delphi51

Sorry, didn't understand that! You should be adding some 4 mm's or .004 m's movements together to get the distance moved in each cycle. How many?

5. Oct 26, 2009

### amandine

I'm just guessing but 1000000 because 1 km is 1000000 mm. For starters, the question doesn't make sense to me.

6. Oct 26, 2009

### Delphi51

up to peak, back to center, down to trough, back to center
4 + 4 + 4 +4
16 mm per cycle.
How many cycles to make a km?

7. Oct 26, 2009

### amandine

How did you know to add 4? Or that it was 16 mm per cycle?

8. Oct 26, 2009

### amandine

62500 cycles because 1 km = 1000000 mm and 1000000 mm / 16 mm = 62500.

9. Oct 26, 2009

### willem2

you already correctly computed 8mm for each cycle for question a.

10. Oct 26, 2009

### amandine

Oh, so is this the answer or is there more?

11. Oct 26, 2009

### Delphi51

Thank goodness for Willem! Yes, the amplitude is 2 mm; don't know where I got the 4 from! You'll have to redo your calc for (d) dividing by 8 instead of 16. Sorry!

12. Oct 26, 2009

### amandine

Dividing by 8 with what? I'm lost. Could you make up an example of the question d and e? I don't understand the questions...

13. Oct 26, 2009

### Delphi51

I fear I have mixed you up! You already did it with the 16.
Just 1000 000/8 is the answer to d.

You can do e in a jiffy after you finish (d) so you know the number of cycles and you already have the time for one cycle.

14. Oct 26, 2009

### amandine

I finished (d) by 1000000 mm / 8 mm = 125000 mm
For (e) would the answer be 125000 mm = 125 m therefore 125 m / 450 m.s = 0.27 s because the number of cycles is 125000 mm or 125 m and the time for one cycle is 450 m.s?

Please correct me if I'm wrong.

15. Oct 27, 2009

### willem2

the answer for d should be in cycles, not mm. This mistake probably caused you
to do the wrong thing in e as well
e) is the time to complete 125000 cycles. you already computed the period in c.

16. Nov 1, 2009

### amandine

The period is the time to complete 125000 cycles? The period being 4x10^-4s is the answer to question e?

17. Nov 1, 2009

### willem2

No, the period is the time to complete 1 cycle.

18. Nov 1, 2009

### amandine

To get the answer to question e do I divide 125000 / 0.0004 to get the time required for a particle on a string to move through a total distance of 1.0 km which would equal 312500000? If this is right then ignore this question about where does the amplitude fit in?