Measuring sound: Maths and graphing skills
Specification references:
•
P6.1.2 Properties of waves
•
WS3.2, WS3.5, WS4.1
Aims
You will be learning how to interpret graphical data to calculate the speed of sound in different materials.
Learning outcomes
After completing this worksheet, you should be able to:
•
use the gradient of different graphs to calculate physical quantities
•
describe the features of sound waves in different materials.
Setting the scene
Sound waves travel at different speed in different materials, depending on their density. Sound travels faster in
water than in air, because water is much denser than air. The speed of sound in air is approximately 330 m/s,
but that also varies depending on how dense the air is. For example, the higher in the atmosphere you go, the
less dense the air becomes.
Metals and other solids are even denser than water, so sound waves can travel very fast through them.
Worked example
The apparatus in the diagram is used to measure the time taken by a sound wave to travel through a copper
rod.
Two microphones attached at either end of the rod are set up to
record signals. Signals are recorded by an audio recording app on
the computer.
One end of the rod is hit by a hammer and the time difference
between the two signals recorded by the microphones is
displayed on the software. By knowing the length of the rod we
can calculate the speed of the sound wave in the copper rod.
Below is a graph of the different lengths of copper rod against the
time taken by the sound wave to travel through the rods.
What is the speed of sound in copper according to the graph above?
Gradient =
change in y value (time)
6.5 × 10−4
=
= 0.000217 = 2.17 × 10−4
change in x value (length)
3.000
length s
= to give the speed of the sound wave. So we need to do an extra
time
t
1
calculation to get the value we want: speed =
gradient
But we need to know rod
v =
1
1
=
= 4615 m/s
gradient 2.17 × 10−4
Task
The graphs below show the time taken for a sound wave to travel through three different materials. Each
measurement was taken following the same procedure as in the worked example.
Lead, gold, and glass rods were used to record the time taken by the sound wave to travel along rods of
increasing length.
Use the three graphs to calculate the speed of sound in lead, gold and glass respectively.
Questions
1
Look at the graph in the task and use the values of the speed of sound in different materials you found to
answer the following questions.
a A trusted source of information gives the speed of sound in lead as 1210 m/s. Does your calculation of
the speed of sound in lead from the graph in the task agree with this accepted value? Explain your
answer.
(3 marks)
b
The students investigating the speed of sound in gold declared that their value of speed of sound in
gold (from the graph in the task) is accurate within a range of ± 25 m/s. A reliable source of information
gives the value of speed of sound in gold as 3240 m/s. Are the results of the group of students in
agreement with the accepted value? Explain your answer.
(4 marks)
c
A reliable source of information gives the value of speed of sound in glass as 4540 m/s. Calculate the
percentage difference between the accepted value and the value of speed of sound in glass you
calculated from graph in the task. Is this difference significant? Explain your answer.
(4 marks)