Name ____________________________
Date ______________________________
POGIL: Wave Speed Equations
When we link two vibrating objects together, the vibration of the first can be passed on to the second.
If we connect many of these objects together, the vibration of the first will be passed to each one in
succession. We call this a wave. We can think of waves as a way of transmitting energy in the form of
vibrations. In this POGIL we will review the terms we use to describe waves & introduce two
equations to calculate the speed of the wave,
v = fλ
&
d
v=
t
Transverse Waves
The picture below shows some transverse waves on a slinky, with various parts labeled. The waves are
initiated by the hand and travel to the right.
crest
amplitude
wavelength
trough
The following terms are used to describe time-based characteristics of the wave.
•
•
•
•
Period: the time it takes for one wave to pass by a point
Frequency: the number of waves that pass by a point each second
Wavelength: the length of one wave
Wave speed: how far the wave moves per unit of time
1. Study the diagram of the transverse wave below, traveling to the right. An observer standing at
point P notes that 5 waves pass by in 10 s.
4m
3m
P
a) On the diagram, label each crest with a C and each trough with a T. How many crest are there
in the wave? How many troughs are there in the wave?
# of crest: __________
# of troughs: __________
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b) What is the amplitude of the wave?
c) What is the wavelength of the wave?
d) What is the frequency of the wave?
e) What is the period of the wave?
f) How far do the waves travel in 10 s? Hint: 5 complete waves pass by in 10 seconds.
g) Use your answer to part f and the speed equation (v=d/t) to calculate the speed of the wave in
10 seconds.
h) Use the wave speed equation (v = f λ) to calculate the speed of the wave.
i) What is the difference between your calculations from parts g & h?
Longitudinal Waves
The picture below shows some longitudinal waves on a slinky, with various parts labeled. The waves
are initiated by the hand and travel to the right.
compression
rarefaction
wavelength
Most of the terms we use to describe transverse waves apply to longitudinal waves as well; period,
frequency, and wave speed have the same definitions.
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2. Study the diagram of the longitudinal wave below. As it is travels to the right, an observer at point
P notes that it takes 0.5 s for one wave to pass by.
3m
P
a) On the diagram, label each compression with a C and each rarefaction with an R. How many
compressions are there in the wave? How many rarefactions are there in the wave?
# of compressions: __________
# of rarefactions: __________
b) What is the wavelength of the wave?
c) What is the frequency of the wave?
d) What is the period of the wave?
e) How far do the waves travel in 10 s? Hint: 20 complete waves pass by in 10 seconds.
f) Use your answer from part e and the speed equation (v=d/t) to calculate the speed of the wave
in 10 seconds.
3. How are speed equation (v=d/t) and the wave speed equation (v = f λ):
a) Similar?
b) Different?
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Problem Solving
4. The diagram below shows a wave and some of its physical characteristics. The speed of the wave is
1 m/s.
0.5 m
9m
a) What kind of wave is this? Explain your answer.
b) What is the wavelength of the wave? Hint: There are 1.5 waves on 9 meters.
c) What is the amplitude of the wave?
d) Use the speed equation (v=d/t) to calculate how far does the wave travel in:
i. 1 s?
ii. 2 s?
iii. 6 s?
e) Use the wave speed equation (v = f λ) to calculate the frequency of the wave.
f) What is the period of the wave?
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