物理演算課
PHYSICS
教授: 陳致曉 老師
助教: 光電所 王煜程
Question 1
The wave function for a traveling pulse is
𝑦 𝑥, 𝑡 =
8
1+(𝑥+4𝑡) 2
where x and y are in meters and the time t is in seconds. In which
direction and with what speed is the pulse propagating?
Question 2
A harmonic transverse wave function is given by
𝑦 𝑥, 𝑡 = (0.850 𝑚) sin(15.3𝑥 + 10.4𝑡)
where all values are in the appropriate SI units.
a. What are the propagation speed and direction of the wave’s travel?
b. What are the wave’s period and wavelength?
c. What is the amplitude?
d. If the amplitude is doubled, what happens to the speed of the wave?
Question 3
A string of length L and mass M hangs freely from a fixed point on
the ceiling.
a. Determine the propagation speed of a transverse wave traveling
along the string at any position y.
(Hint: The tension is not constant throughout the string. The tension
at any point along the string is equal to the weight (g dm) of the string
below that point.)
b. Determine the time required for a transverse pulse to travel the
entire length of the string.
Question 4
As the figure, a simple harmonic oscillator is attached to a rope,
creating a transverse wave of wavelength 7.47 cm. At the other end of
the rope is a pulley and a hanging block of mass 6.30 kg. The
oscillator has an angular frequency of 2340 rad/s and an amplitude of
34.6 cm.
Question 4
a. What is the linear mass density of the rope?
b. If the angular frequency of the oscillator doubles, what properties
(speed, angular wave number, amplitude) of the wave must change?
Give the new values of these properties.
c. If the frequency remains at its original value but the mass of the
hanging block is doubled, what properties of the wave must change?
Give the new values of these properties.
Question 5
An oscillating lever delivers a maximum power of 0.500 kW to a
string with linear mass density of 1.50 × 10 −2 kg/m that is under 125
N of tension. What is the maximum angular frequency of the lever
that will result in the generation of sinusoidal waves with an
amplitude of 3.00 cm?