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Physics 112 HW23
Due Monday, 17 November 2014
U1-WM2: (Wolfson, Ch. 14 Prob. 23) A wave’s displacement (motion about equilibrium
position) is given by y(x, t) = 1.3cm cos(0.69x + 31t), where t is in seconds.
a) What is the amplitude of this wave?
b) What is the wavelength of this wave?
c) What is the period of this wave?
d) What is the speed of this wave?
e) In which direction is the wave propagating?
U1-WM4: (Wolfson, Ch. 14 Prob. 46, edited) The
figure at right shows a simple harmonic wave
traveling on a long string at time t = 0 and later at t =
2.6 seconds.
a) Write the mathematical description y(x, t) for this wave.
b) Find the instantaneous vertical velocity and acceleration of a piece of string the moment it
reaches its maximum height.
c) Find the instantaneous vertical velocity and acceleration of a piece of string the moment it
reaches its equilibrium position (the middle) and is going down.
d) Find the instantaneous vertical velocity and acceleration of the piece of string at x = 9 cm
when t = 2.0 seconds.
U1-WM7: A transverse sinusoidal wave traveling in the positive x direction on a horizontal
string has an amplitude of 15.0 cm, a wavelength of 40.0 cm, and a frequency of 8.00 Hz. The
vertical displacement of the string at t = 0 and x = 0 is +5.0 cm.
a) Find the wave number, period, angular frequency, and speed of the wave.
b) Determine the phase constant of the wave and write the expression for the wave y (x, t),
and sketch what the wave looks like (y vs. x graph) at t = 0 seconds.
c) What is the vertical displacement of the wave at x = 5 cm and t = 4 seconds?
U1-WM10: Below is a snapshot at t = 0 (y vs. x graph) of an oddly-shaped pulse traveling down
a string to the right (positive x direction) at 2 m/s. Draw a y vs. t graph of the point on the string at
x = 7 m.
y (cm)
2
2 m/s
1
x (m)
-2
-1
1
2
3
-1
-2
(over)
4
5
6
7
U1-WM11: Below is a y vs. t graph of the x = 0 point on a horizontal string with another pulse
traveling down on it. The pulse travels down the string to the left (negative x-direction) with a
speed of 1 m/s. Draw a snapshot (y vs. x graph) of this pulse at t = 1 s.
y (mm)
2
1
t (s)
-2
-1
1
2
4
3
5
6
7
-1
-2
U1-WM6: (Wolfson 1st ed., Ch. 14 Ex. 54 modified slightly) A travelling wave on a
very long taut wire is described by the equation y = (1.5cm) sin(0.10cm-1 x – 560s-1 t),
where x is in cm and t is in seconds. If the wire tension is 28N, what are
a) the amplitude,
b) the wavelength,
c) the period,
d) the wave speed,
e) the maximum transverse acceleration (magnitude) of any part of the wire far from
an end?
U1-SW6: Below is a y vs. x graph of two “square” pulses at t = 0s traveling to the right
(+x) down a rope with a speed of 1 m/s. For x ≥ 6 m, the rope has ¼ the mass density
that it does for x < 6m. Draw snapshot graphs (y vs. x) at
a) t = 2.5s
y (mm)
b) t = 4s
2
1 m/s
1
×
1
2
-1
-2
(over)
3
4
5
6
x (m)
7
8
9
10
11
12
13