Query_12

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course Phy 242

7/10 10 pm

Question: `q**** Query introductory set six, problems 11-13 **** given the length of a string how do we determine the wavelengths of the first few harmonics?

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Your Solution:

The wavelengths of a string with both ends in a fixed postion are 2*L/n where n can be any positive integer.

@&

You've quoted a formula.

This should be reasoned out from basic principles.

*@

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Given Solution: `q** As wavelength decreases you can fit more half-waves onto the string. You can fit one half-wave, or 2 half-waves, or 3, etc..

So you get

1 half-wavelength = string length, or wavelength = 2 * string length; using `lambda to stand for wavelength and L for string length this would be

1 * 1/2 `lambda = L so `lambda = 2 L.

For 2 wavelengths fit into the string you get

2 * 1/2 `lambda = L so `lambda = L.

For 3 wavelengths you get

3 * 1/2 `lambda = L so `lambda = 2/3 L; etc.

Your wavelengths are therefore 2L, L, 2/3 L, 1/2 L, etc..

FOR A STRING FREE AT ONE END:

The wavelengths of the first few harmonics are found by the node - antinode distance between the ends. The first node corresponds to 1/4 wavelength. The second harmonic is from node to antinode to node to antinode, or 4/3. the third and fourth harmonics would therefore be 5/4 and 7/4 respectively. **

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Question: `q**** Given the wavelengths of the first few harmonics and the velocity of a wave disturbance in the string, how do we determine the frequencies of the first few harmonics?

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Your solution:

To determine the frequencies of the first few harmonics, we just divide the velocity by the wavelength.

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Given Solution:

`a** The frequency is the number of crests passing per unit of time.

We can imagine a 1-second chunk of the wave divided into segments each equal to the wavelength. The number of peaks is equal to the length of the entire chunk divided by the length of a 1-wavelength segment. This is the number of peaks passing per second.

So frequency is equal to the wave velocity divided by the wavelength. **

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Self-critique (if necessary):ok

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Question: `q **** Given the tension and mass density of a string how do we determine the velocity of the wave in the string?

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Your solution:

V = sqrt [tension / (mass/length) ]

@&

This formula is OK; I don't expect everyone to be able to reason this result out from basic principles.

*@

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Given Solution:

`a** We divide tension by mass per unit length:

v = sqrt ( tension / (mass/length) ). **

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Question: `q**** gen phy explain in your own words the meaning of the principal of superposition

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Your solution:

n/a

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Given Solution:

`a** the principle of superposition tells us that when two different waveforms meet, or are present in a medium, the displacements of the two waveforms are added at each point to create the waveform that will be seen. **

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Question: `q **** gen phy what does it mean to say that the angle of reflection is equal to the angle of incidence?

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Your solution:

n/a

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Given Solution:

`a** angle of incidence with a surface is the angle with the perpendicular to that surface; when a ray comes in at a given angle of incidence it reflects at an equal angle on the other side of that perpendicular **

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&#Good work. See my notes and let me know if you have questions. &#