PASCO WA-9867 Sine Wave Generator - Manual (Page 19)

Model No. WA-9867 Experiment 1: Standing Waves In Strings
19 ®
Part II:
Wave Speed and String Density
Theory
As stated in Equation 1, the speed of any wave is related to the wavelength and the frequency. For
a wave on a string, the speed is also related to the Tension (F) in the string, and the linear density
(
µ) of the string, as shown by
(eq. 2)
The linear density (
µ) is the mass per unit length of the string. The Tension (F) is applied by the
hanging a mass (m), and is equal to the weight (mg) of the hanging mass.
For this part of the experiment, you will always adjust the frequency so that the wave vibrates in
four segments, thus the length of the string will always equal two wavelengths (L = 2
λ).
In this case F = mg and L = 2
λ; these equations can be combined with equations 1 and 2 to show
(eq. 3)
where:
f = driving frequency of the Sine Wave Generator
g = acceleration due to gravity
m = total hanging mass
L = length of string (vibrating part only)
µ = linear density of the string (mass/length)
v
F
µ
--- =
L
l
String
String
Vibrator
Hanging
Mass
Pulley
f
2 4g
µL 2
---------- m =