Displacement-Distance versus Displacement-Time Graphs Learning object

1. Displacement-distance and Displacement-time Graphs
1.
a. What is the amplitude of this graph?
b. Can the wavelength be determined from this graph? If so, calculate the
wavelength.
c. Can a wave number be determined from this graph? If so, calculate the
wave number
d. Can the period be determined from this graph? If so, calculate the
period.
e. Can an angular frequency be determined from this graph? If so,
calculate the angular frequency.
f. Can a phase constant be determined from this graph? If so, calculate
the phase constant.
g. Can a speed be determined from this graph? If so, calculate the speed.
h. Write an equation for the wave.

2. 2.
3.
a. What is the amplitude of this graph?
b. Can the wavelength be determined from this graph? If so, calculate the
wavelength.
c. Can a wave number be determined from this graph? If so, calculate the
wave number
d. Can the period be determined from this graph? If so, calculate the
period.
e. Can an angular frequency be determined from this graph? If so,
calculate the angular frequency.
f. Can a phase constant be determined from this graph? If so, calculate
the phase constant.
g. Can a speed be determined from this graph? If so, calculate the speed.
h. Write an equation for the wave.

3. Answers
1.
a. The amplitude of this wave is the absolute value of the maximum
displacement from its equilibrium position. In this graph, A=0.15m.
b. The wavelength is the shortest distance over which a wave repeats. It
is possible to measure the wavelength of this wave because this graph
shows the displacement of a wave over a distance. By measuring from
the equilibrium position at zero to the next equilibrium position at 2, I
can calculate that 𝜆 = 2𝑚
c. Yes. The wave number, 𝑘, is determined by the equation 𝑘 = 2𝜋/𝜆,
and because we know the value of 𝜆, we can determine 𝑘. 𝑘 =
2𝜋
2
= 𝜋
d. No the period cannot be determined from the graph because period is
measured in seconds and time is not a variable on the graph.
e. No, an angular frequency cannot be determined from the graph
because 𝜔 = 2𝜋/𝑇, and T (period) cannot be determined from the
graph.
f. Yes, a phase constant can be determined from this graph. In this case,
the phase constant is zero because it is a sine wave that starts at the
origin, and is not displaced initially. As long as the equation we write
in part h is a sine equation, the phase constant of this graph is equal to
zero.
g. No, speed cannot be determined from this graph alone because 𝑣 =
𝜆𝑓, and because time is not a variable in this graph, the frequency, 𝑓,
cannot be determined from the graph.
h. This equation of this wave is the displacement of the wave 𝐷(𝑥) as a
function of the position, 𝑥, in the form 𝐷( 𝑥) = 𝐴 sin(𝑘𝑥). After
collecting our answers from parts a to c, the equation of the graph is
𝐷( 𝑥) = 1.5sin 𝜋𝑥
2.
a. The amplitude of this wave is the absolute value of the maximum
displacement from its equilibrium position. In this graph, A = 1cm =
0.01m
b. No the wavelength cannot be determined from this graph. The
wavelength is the distance in which the wavelength repeats itself, and
since a displacement-time graph does not give information about the
distance of a wave, the wavelength cannot be determined from this
graph.
c. No, a wave number cannot be determined as the equation for the
wave number is 𝑘 = 2𝜋/𝜆, and since the wavelength, 𝜆, cannot be
determined, neither can the wave number.
d. The period of a wave is the time it takes to complete one full cycle, and
in this graph T= 2s.
e. Since 𝜔 = 2𝜋/𝑇, the angular frequency for this wave, 𝜔 = 𝜋
f. Yes, a phase constant can be determined from this graph. In this case,
the phase constant is zero because it is a sine wave that starts at the

4. origin, and is not displaced initially. As long as the equation we write
in part h is a sine equation, the phase constant of this graph is equal to
zero.
g. No, speed cannot be determined from this graph alone because 𝑣 =
𝜆𝑓, and because time is not a variable in this graph, the frequency, 𝑓,
cannot be determined from the graph.
h. This equation of this wave is the displacement of the wave 𝐷(𝑡) as a
function of the time, 𝑡, in the form 𝐷( 𝑡) = 𝐴 sin(𝜔𝑡). After collecting
our answers from parts a to c, the equation of the graph is 𝐷( 𝑡) =
0.01 sin 𝜋𝑡
The graphs were taken from Physics for Scientists and Engineers - 1e written by
Hawkes, Iqbal, Mansour, Milner-Bolotin, and Willia.