Physics 1021
Laboratory #2
9
Standing Waves
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Standing Waves
Waves on strings are transverse waves. When a string is vibrating at its
fundamental frequency, the wave pattern looks like the one shown below.
𝑨
𝑵
𝑵
𝐿=
𝜆
2
There is an antinode 𝑨 at the middle where the displacement of the string is at a
maximum. There are nodes 𝑵 at the fixed ends of the strings where there is no
displacement of the string.
For strings vibrating at a frequency other than the fundamental, the standing
wave pattern may resemble the one shown below.
1⁄2 𝜆
1⁄2 𝜆
1⁄2 𝜆
1
𝐿 = 12𝜆
In this picture, there are 1½ wavelengths present on the string. If we are able to
measure the length of the string, it is straightforward to determine the
wavelength.
For all waves, the speed is given by
𝑣 = 𝑓𝜆
(1)
where 𝑓 is the frequency of the oscillation and 𝜆 is the wavelength of the
standing waves.
For waves on a string, the wave velocity is also given by
𝑣=√
𝑇
𝜇
(2)
Physics 1021
Laboratory #2
Standing Waves
10
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where 𝑇 is the tension in the string and 𝜇 is the mass per unit length.
Combining the above equations gives the wavelength of the wave on the
string as
1
𝑇
𝜆= √
𝑓 𝜇
.
(3)
Physics 1021
Laboratory #2
Standing Waves
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Prelab Questions
These questions need to be
completed before entering the lab.
Please show all workings.
Marker’s
Initials
Prelab 1
Referring to the picture shown and the previous pages:
a) Label all the nodes (𝑵) and antinodes (𝑨) on the diagram.
b) How many nodes are present?
c) How many antinodes are present?
d) How many wavelengths are present?
e) If the string is 2.0 m long, what is the wavelength?
STAPLE YOUR PRE-LAB TO THIS PAGE
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Physics 1021
Laboratory #2
12
Standing Waves
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Name and Student Number:
___________________________________
Date:
___________________________________
Partner:
___________________________________
QUESTION 1:
Table 1:
𝒎
(kg)
𝑾
(N)
∆𝒙
(m)
number of
wavelengths
CHECKPOINT:
To be signed after completing the first row of Table 1.
𝝀
(m)
𝝀𝟐
(m2)
Physics 1021
Laboratory #2
Standing Waves
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QUESTION 2:
QUESTION 3:
Table 2:
Be sure to include a printout of your Tension vs Wavelength Squared graph.
Value
Slope
Uncertainty
Units
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Physics 1021
Laboratory #2
Standing Waves
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QUESTION 4:
QUESTION 5:
QUESTION 6:
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Physics 1021
Laboratory #2
Standing Waves
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QUESTION 7:
QUESTION 8:
Staple graph(s) to the
reverse side of this page.
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