Lab: Resonance in Closed-End Tubes
Purpose
To determine the resonant length of a closed-end air column for tuning forks of different fundamental frequencies.
To calculate the frequency of the tuning forks experimentally from the resonant length and the temperature of the air
in the column.
Theory
Resonance is the increase in amplitude of a wave when the frequency of the wave source corresponds to the natural
frequency of the system in which the wave travels. For a closed-end air column, resonance is observed as the loud
sound heard when a standing wave pattern with a node at the closed end and an antinode at the open end develops
in the air column. The shortest resonant length, L1, corresponds to ¼ of the wavelength, , of the wave source.
  4L1
Longer resonant lengths have an additional ½ wavelength as shown in the diagram below. The second resonant
length should be triple the shortest resonant length.

The speed, v, of sound in air can be calculated from the temperature, Tc, of the air in Celsius degrees according to
the equation
v  331m / s  0.59
m/s
o
C
Tc
The experimental frequency of the sound wave can then be calculated using the universal wave equation
v  f

f 
v

The absolute error is the difference between the frequency of tuning fork, factual and the experimentally determined
frequency fexp . The relative (percent error) is the ratio of the absolute error to the actual frequency factual
|f
f |
%Error  actual exp 100%
f actual

Materials
Procedure
tuning forks (3)
water

graduated cylinder
ruler
long glass tube
thermometer
Preparation
 A graduated cylinder was filled with water and the glass tube was placed in the graduated cylinder.
Resonant Length
 A tuning fork was struck with a mallet and held about 1 cm above the end of the glass tube.
o DO NOT ALLOW THE TUNING FORK TO TOUCH THE GLASS TUBE – THE GLASS WILL BREAK
 The tuning fork and glass tube were slowly raised and lowered together by one student while listening carefully
for the sudden increase in volume of the sound from the tube.
 When the resonant length was found, the tube was held in place while another student measured the length of
the air column (the distance from the top of the water in the graduated cylinder to the top of the glass tube).
 This procedure was repeated for two different tuning forks.
Temperature
 The temperature of the air in the area used was measured using a thermometer or digital temperature probe.
Results

Temperature of the air =_____________
Table 1. Minimum resonant lengths of two tuning forks and the corresponding calculated vales.
ACTUAL VALUE
Tuning Fork Frequency
factual (Hz)
EXPERIMENTAL VALUES
Resonant Length
L (m)
Wavelength
 (m)
ERROR ANALYSIS
Frequency
fexp
Absolute Error
| factual – fexp | (Hz)
Sample Calculations

Speed of sound from temperature of the air

Wavelength from the resonant length

Frequency from experimental speed and wavelength

Absolute error in frequency

Relative error in frequency
Evaluation
Suggest ways to improve this experiment other than testing more tuning forks.
Relative Error
%E