The physics of wave properties on a string

[amandine]

Homework Statement

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?

Homework Equations

v = f lambra
t = 1/f
time = d/v

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.

 

[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.

 

[amandine]

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.

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

 

[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?

 

[amandine]

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?

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

 

[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?

 

[amandine]

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?

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

 

[amandine]

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?

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

 

[willem2]

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

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

 

[amandine]

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

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

 

[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!

 

[amandine]

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!

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...

 

[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.

 

[amandine]

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.

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.

 

[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.

 

[amandine]

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.

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

 

[willem2]

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

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

 

[amandine]

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

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?