The speed of sound (c) can be calculated using a graph instead of by formula.
Calculations Calculate the reciprocal of the frequency .
a
Tabulation of Data Table 11.2
f / Hz l / m
1 f > Hz1
Graph Plot a graph of length (l), measured in metres, against , measured in , with length on the y-axis.
1 f
Use Graph
Speed of sound can be calculated from the graph. If the length is on the y-axis and on the x-axis, then speed of sound in air is 4 times the slope of the line of best fit Explanation
1 f
(c 4 slope) .
Based on the equation for speed of sound we get: Using the equation of the line
Note This experiment can be used to demonstrate resonance.
y mx c, c 4f(l 0.3d)Ql c
4 a
1 f b 0.3d
given that c 0.3d , it is clear that speed of sound in air is 4 times
the slope. Note: The ‘c’ from the line equation is different from the ‘c’ in the experiment, which means speed of sound.
Hz1
1 f b
The Fundamental Frequency of a Stretched String
The fundamental frequency of a stretched string (or wire) depends on three factors:
(i) its length (l) (ii) the tension in it (T) (iii) its mass per unit length .
(m)
Experimentally the following relationships have been found: (i)
f r 1 l
(ii) (iii)
f r 1T, when l and are fixed , when T and l are fixed.
