# Help on my Final: Thermodynamics, optics, waves

1. Jun 2, 2006

### kooaznboi1088

Hey I'm a junior this year and physics finals are coming up. I managed to get B- on all 3 quarters up until now. And If i cannot get atleast a 92% on my final, I will end up with a C for the year :surprised. So any kind souls out here who can help please it will be appreciated with such a gratitude like you will never believe.

Anyway I mostly need help with word problems so here goes.
A 20.0 cm-amplitude wave travels along a 40.0cm long string from the left end to the right end of the string. If the string has a mass of .01 kg and is under a tension of 500.0 N.

a. Find the speed of the wave on the string.

b. If the string is fixed at both ends, this wave will be reflected with the same amplitude, frequency, and speed, but traveling in the opposite direction. Plucking the string continuously makes a standing wave interference patttern at the resonant frequency because the incident wave traveling to the right will interfere with the reflected wave traveling to the left. Let the incident wave traveling to the right by Y1. and the reflected wave traveling to the left be Y2. Find the frquency of the standing wave corresponding the the 7th overtone.

c. Sketch the standing wave for the 7th overtone.

d. Find the wavelength at the fundamental freequency.

e. Find the fundamental frequency

f. From d and e, write the wave function for Y1 and Y2.

g. Find the resultant disturbance produced when Y1 and Y2 are superimposed.

H.Sketch waveform graph for Y1, showing atleast 4 cycle.s

i. Sketch vibration graph for Y1 showing atleast 4 cycles.

Sorry for such a long problem. But i missed ALL of that section on the test intially. So I have no idea where to start :(.

Last edited: Jun 2, 2006
2. Jun 2, 2006

### Tide

You need to realize that no one here can help you until you've at least shown some effort of your own to solve the problem.

3. Jun 2, 2006

### kooaznboi1088

ok heres what I have so far
a. SqRoot(T/(m/l)= Frequency so I get Sqroot(500/(.01/.4)) * (.4) = 56.6 m/s. But thats obviosly incorrect because I got it wrong.

b. nv/2l= 7(56.6)/2(.4)= 49.5 cycles/s

c. No idea where to begin

d. 1/7 * 495/7 = 7(56.6)/2(.4)=.8m

e. 70.7 cycles/s

f. no idea where to begin

g. no idea where to begin

h. no idea where to begin

i. no idea where to begin

sorry for the lack of work but i really do not know how to do physics. 197/485 was the score i recieved for this test.

Last edited: Jun 2, 2006
4. Jun 2, 2006

### Hootenanny

Staff Emeritus
Question (a)

You said the equation is;

$$f = \sqrt{\frac{T}{\frac{m}{L}}}$$

You were half right, infact the above equation is for velocity. So;

$$v = \sqrt{\frac{T}{\frac{m}{L}}}$$

Just plug your numbers in and away you go.

Question (b)

Almost there, however note that the 7th overtone is the 8th harmonic, where n in your equation is the nth harmonic.

Question (c)

How many nodes does the 7th overtone have? What will the amplitude of the anti-nodes be?

Question (d)

The fundemental frequency is given by;

$$f_{0} = \frac{v}{2L}$$

Use the wave equation to manipulate the above equation and you should find that the velocity term drops out and you are left with a function for wavelength in terms if string length.

Question (e)

You may want to check this in light of the above corrections.

Question (f)

Do you know the standard form for a wave equation for a traveling wave?

Question (g)

Do you know the standard form for a wave equation for a standing wave?

___________________________________​

~H

Last edited: Jun 2, 2006
5. Jun 3, 2006

### kooaznboi1088

Thanks I get. A, B, D, E

C. So I just sketch 8 crests and 8 troughs right?
I still do not get
F, G and H and I

I don[t konw how to sketch the equations.

Last edited: Jun 3, 2006
6. Jun 4, 2006

### Hootenanny

Staff Emeritus
The 7th overtone has seven nodes and eight antinodes, a standing wave always has one more antinode than it has nodes.

From question, I would say that the question requires you to write an equation that will describe the verticle displacement is terms of horizontal displacement and time. Now the standard wave equation for an ideal string is given by;

$$y(x,t) = A\sin\frac{2\pi}{\lambda}(x - vt)$$

This can be manipulated to represent vertical acceleration and vertical velocity. All that you now need to do is plug your numbers in. The same can be done for the reflected wave. However, note that the reflected wave is travelling in the opposite direction, therefore its velocity will be negative.

A standing wave on a string can be represented by the equation;

$$y(x,t) = A\sin\omega_{n}t\sin\frac{nx\pi}{L}$$

Where n is the nth harmonic and;

$$\omega_{n} = v\cdot \frac{n\pi}{L}$$

~H

7. Jun 8, 2006

### kooaznboi1088

Hey thanks. One more problem really quickly. Finals are tommorow.

The density of diamond, a form of carbon, is 3520 kg/m^3. How many carbon atoms are there in a solid diamond sphere with a radius of .03mm?

Work so far :
V=R^3pie=(.033)^3pie
PV=nRT
Density*Volume=Mass= 3520*(.033)^3 pie

8. Jun 8, 2006

### Hootenanny

Staff Emeritus
One correction, the volume of a sphere is given by;

$$V = \frac{4}{3}\pi R^3$$

Also, 0.03mm = 3x10-5 kg. You need to be in SI for this calculation. You cannot use the ideal gas equation (pV= nRT) because carbon is not an ideal gas. This step;
Is correct (except you need to modify your numbers with respect to the above calculation). You now have a mass of carbon in kg.

I think it is safe to assume that all the carbon is the carbon-12 isotope, so how heavy is a carbon-12 isotope in atomic mass units?.

How many kilograms in an atomic mass unit?

Apologies if this it too late for your final today, but were are at slightly different time zones here in the UK.