Lab 5 Mechanical Waves!
!
Objective
The purpose of this lab is to examine various properties of a mechanical wave. Specifically, we
will look at the relationship between the wave speed, the wavelength, and the frequency of a
harmonic wave. Furthermore, we will look at how these properties relate to the physical property
of a medium.
Equipment
Function generator, frequency counter, mechanical wave driver, pulley.
Background
We start with a medium. This is the string.
fixed
end
oscillator
end
When a simple harmonic wave is created, it has a sinusoidal form. It also travels away from the
source at some speed.
wave speed
fixed
end
oscillator
end
When this wave strikes an interface of any kind, it will be reflected and transmitted. In this
experiment, it will be reflected since the wave will strike a fixed end. The reflection will have the
same speed. The reflection will also contain a phase shift of π or 180°.
wave speed
fixed
end
oscillator
end
wave speed
When our wave is reflected, the reflected wave travels over our original wave. These two wave
overlap and superimpose. The result is just a sum of the two waves. This is called superposition.
total wave
oscillator
end
fixed
end
If the number of half-wavelengths fits into the length of the string, the two waves will always add to
each other to form a larger amplitude. This forms what is called a standing wave. This is what is
shown in blue above.
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Experiment: Wave Speed
The reverse of this result is that when we have standing waves, the length of the medium will be a
multiple of half-wavelengths of the wave itself.
1
L=n λ
2
Let’s use this fact to find the wave speed. The wave speed relates to the wavelength through the
frequency.
v = λf
What we will do is count the number of half wavelengths and measure the frequency that is
required to produce the standing waves.
λ=
v
2L
=
f
n
⇒ f =
v
n
2L
Use a 50 gram mass to hold the string taut. Set up standing waves with the number of halfwavelengths from 1 to 6. Record the frequencies required to produce these standing waves. Plot
the frequency as a function of the number of half wavelengths. Use the slope to find the wave
speed.
Flick the string and estimate the speed of the pulse. Compare it to your result.
Experiment: Tension
If you were to change the weight at the end of the string, you result will be different. The wave
speed depends also on the characteristics of the medium. In this case, it depends on the tension
and the density of the string in a more complex manner.
v=
T
µ
The density is constant so we can’t vary it, but we can change the tension. We can’t measure the
wave speed directly so let’s measure the frequency. What about the wavelength? Let’s keep it
constant by producing only standing waves of with n = 3.
λ=
2L
2L
=
n
3
What we’ll do is measure the frequency as a function of the tension.
f =
3
2L µ
T
Use the data to find the linear density of the string. Plot the frequency as a function of the
squared of the tension. It is suppose to be 0.1583 grams/meter. Compare this to your result.
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