Two plots concerning a sinusoidal traveling wave on a wire are shown above. The

Question

Two plots concerning a sinusoidal traveling wave on a wire are shown above. The first plot is a snapshot (at a specific time) of the wire as a function of position from x=0 to x=1156 cm. The second plot is of the time dependence of a specific point on the wire from t=0 to t=0.4053 s. Pay attention to the units of the graphs, and note that the patterns you see repeats itself an integer number of times in each graph. The general form of the wavefunction for this traveling wave is given by: y(xchar3B.pngt)=Asin(kx?char21.pngt)

1) Find the wavelength of the wave.

2) Find the period of the wave.

3) Find the frequency of the wave.

4) Find the angular frequency of the wave.

5) Find the wave number of the wave.

6) Find the speed of the wave.

7) Find the maximum speed of a particle on the wire.

8) If the tension in the wire is 53.00 N, what is the linear mass density (mass per unit length) of the wire?

Explanation / Answer

a) From first graph, the wavelength is the length of single wave (in
cm). Pick a starting point on the wave, such a peak or a valley or a
zero-crossing. Now move to the right and find the first place where
that exact point occurs again. The wavelength is the horizontal
distance between those points, expressed in the units of the graph. It
is the distance over which the wave repeats itself.

Wavelength (L) = 1156/6=192.67 cm

b) Now do the same on the second graph to find the period of the wave.
Note that the units are now in seconds. The period is the time over
which the wave repeats itself.
Period (T) =0.4053 /3 =0.1351

c) The frequency is just the inverse of the period.

f = 1/T = 7.4 Hz

d) Angular frequency = w = 2pi*f = 2pi*7.4 =46.51 rad/s

e) Wave Number = k = 2pi/L = 0.033 cm^-1

f) The speed of the wave = vwave = w/k = 9321.74 cm/s = 1426.2 m/s

g) Maximum speed = Aw = 107.2*A cm/s

h) Mass density = T/v^2 = 53/1426.2^2 = 2.6*10^-5 kg/m

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