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# Physics/Waves

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Question

waves
1. Write down an expression for the wavelength lambda as a function of the length of the string for each of the four harmonics shown on the left.
2. From the expressions above, find the expression for the wavelength of the n-th harmonic as a function of L.
3. Determine the expression for the frequency f of the n-th harmonic as a function of and L,v the wave speed.

4. A string of linear mass density of 0.0169 g/cm is attached at one end to a wall. At the other end, it passes over a massless pulley and is attached to a hanging mass. Determine the tension in the string and the wave speed if the hanging mass is
a. 200 g
b. 100 g

5. Instead of being attached to a wall, the string is attached to a motor generating sinusoidal wave. The length of string between the motor and the pulley is 2.5 m. Using the information found in the previous questions, find the frequencies for the first five modes. Take that opportunity to fill in the theoretical parts of the lab report tables.

Answer
Hello Nick,

1a. Lambda = 2*L
1b. Lambda = L
1c. Lambda = 2L/3
1d. Lambda = L/2

2. The values of Lambda above could be written 2*L/1, 2*L/2, 2*L/3, and 2*L/4. So the general expression they're asking
for is Lambda = 2*L/n.

3. It will help to think first about the period T, which is 1/f. The wavelength, lambda, is the distance the disturbance travels during the period, or the time T.

OK now, watch this carefully: Lambda is a distance, period is the time to complete an oscillation, and velocity is distance/time. So the velocity of the disturbance v = lambda/T (or v = lambda*f).

Considering when n = 1, look up at 1a above, and put 2*L in for lambda in the velocity
formula: v = 2*L/T
Since T = 1/f, v = 2*L*f or f = 2*L/v

Now look at number 2 above and substitute the general expression for lambda into the velocity formula to yield a general expression for frequency.
v = (2*L/n) / T = (2*L/n) / (1/f) = 2*L*f/n or
f = v*n / (2*L)

4. Tension = the weight of the hanging mass. For convenience, determine the weight for parts a and b in the units kg.m/s^2 instead of Newtons.

This formula is an experimental result: velocity = sqrt(tension/linear mass density)
Convert the units of the linear mass density to kg/m and plug in tension and linear mass density for parts a and b.

5. For this question, L = 2.5 m. It's unclear if the same string and weights as used in question 4 are to be assumed. If so, plug in the data and determine values for v with the 200 g and 100 g weights. Use the formula
f = v*n / (2*L) with n = 1 thru 5

But then I don't know anything about "the lab report tables".

I hope this helps,
Steve

Physics

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#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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