11

Resonance
U75-4 The fundamental frequency of vibration of a string with both ends fixed is 100 cycle/s.
Under the same conditions, except the length of the string is reduced to half, what will be the
new fundamental frequency of vibration?
C A. 25 cycles per sec B. 50 cycles per sec C. 200 cycles per sec D. 400 cycles per sec

U77-16 A string of length l is fixed at both ends. The mass per unit length of the string is m. If the
tension in the string is T, the frequency of vibration of the string will be proportional to
T 1 T 1 l 1 m
B A. l B. C. D.
m l m T m l T

U77-17 A 50 Hz (cycle/sec) vibrator is used to set up stationary transverse waves on a light string.
If the distance between two successive nodes of the stationary waves is 47 cm, find the velocity
of propagation of the transverse waves on the string.
B A. 23.5 m s–1 B. 47 m s–1 C. 94 m s–1 D. 188 m s–1

U78-12 The fundamental frequencies of an open pipe and a closed pipe were found to be equal. The
ratio of the length of the open pipe to that of the closed pipe was
C A. 4: 3 B. 4: 1 C. 2: 1 D. 1: 2

U82-20 If various sounding tuning-forks (of different frequencies f ) are held

separately over the open end of a tube filled with water, resonance are
obtained at some positions as the level of water is gradually lowered or
raised, as shown in Fig.U82-20, where l is the length of air column of the
first resonance heard. Which of the graphs of 1/f against l shown best
illustrates the results from the experiment? Fig.U82-20
B A.1/f B. 1/f C.1/f D. 1/f E. 1/f

0 l 0 l 0 l 0 l 0 l

U83-P2a What do you understand by resonance of sound?

Besides sound, what other physical entities that would have resonance effects?
(b) A source of sound of frequency 250 Hz is used with a resonance tube, closed at one end, to
measure the speed of sound in air. Strong resonance is obtained as tube lengths of 0.30 m
and 0.96 m. Find (i) the speed of sound, and (ii) the end-correction of the tube.
[330 m s–1; 0.03 m]

U84-7 A resonance tube opens at both ends and responding to a vibrating turning fork has _____.
E A. a central node B. a central antinode C. an odd number of nodes
D. an even number of nodes E. an odd number of nodes + antinodes

U94-17 In a resonance experiment using a resonance tube and a tuning fork, when the length of the
resonance tube is 19 cm and 52 cm respectively, it is in resonance with the tuning fork. Find the
frequency of the tuning fork if the speed of sound is 330 m s–1.
A A. 500 Hz B. 480 Hz C. 440 Hz D. 350 Hz

U97-P7a Compare and interpret the differences of

(i) the number of overtones, and
(ii) the phase difference between the incident wave and the reflected wave between a closed
pipe and an opened pipe.
(b) The frequency of the first overtone of a closed pipe is just equal to the frequency of the
fundamental tone of an opened pipe. If the closed pipe is 0.5 m in length and the instant
speed of sound in the air is 340 m s–1, find the length of the opened pipe and the frequency
of its fundamental tone.
(c) Explain how you can use an opened pipe to find the speed of sound in the air.
[Note: end-correction is not necessary] [0.33 m; 510 Hz]

Prepared by UCSCAM Resonance

Arranged by TAGoh, SYOh, JMTsu, SJChew Copyright
 12
U93-18 Fig.93-18 shows the three possible modes of vibrations of a l
A
string of length l. The ratio of the frequencies of the sounds produces
by the vibrating string corresponding to the vibrations shown in a,b B
and c is fa : fb : fc = ___________
1 1 1 1 C
C A. : :1 B. 1: :
3 2 2 3 Fig.U93-18
C. 1: 2: 3 D. 3: 2: 1

U98-P7 A string of mass 100 g is 10 m in length. One of its ends is fixed and the other is pulled by
a weight of 144 N.
(a) If the string is vibrated with an amplitude of 0.5 m at the point 1 m from the fixed end, find
the speed, wavelength, as well as period of the wave produced and also write down the wave
equation.
(b) If the string is disturbed separately at its two ends to produce two pulses which move in
opposite directions and the interval of the two pulses is 0.04 s, then
(i) where will the two pulses meet on the string?
(ii) what are the three lowest frequencies of the stationary waves on the string?
(Hint: speed of wave on string, v = (T/)
[120 m s–1, 4 m, 0.03 s; 7.44 m from the first pulse; 6 Hz, 12 Hz, 18 Hz]
U2k1-9 A resonance tube is a closed tube. When the frequency of a tuning fork is the same as the
vibrating frequency of the air column in the tube, resonance would occur. A tuning fork is now
resonating with a resonance tube when the air column in the tube is 49.8 cm high. If the speed of
sound is 340 m s–1, find the frequency of the tuning fork.
A A. 512 Hz B. 440 Hz C. 256 Hz D. 128 Hz

U2k06-P6 An experiment is set up as shown in Fig.U2k06-P6, where F

is a tuning fork, S is a meter ruler, R is a transparent glass tube, F
V is a water reservoir and P is a soft rubber tube. Firstly,
connect the reservoir to the glass tube with the soft rubber tube. S
Place the reservoir at a low position and fill it with water, then R V
slowly raise the reservoir. Hold a tuning fork over the open end P
of the glass tube and strike it with a rubber mallet to make it
vibrate. These will cause the air column in the glass tube to
vibrate and a soft sound can be heard. Slowly move the
reservoir downward until the resonance occurs and a loud note
is heard. Record the water level in the glass tube. Fig.U2k06-P6
(a) What is the purpose of this experiment? [2%]
(b) In this experiment, in what direction should the vibration of tuning fork be
pointing in order to obtain the final resonance? Why? [3%]
(d) A student is using an 80 Hz tuning fork in the experiment. If the length of air column
for resonance is 98 cm, determine the speed of sound in air. [314 m s–1] [3%]

U2k10-15. Which of the following diagrams shows the fundamental mode of resonance in a closed pipe?
A A. B. C. D.

U2k12-20 An open pipe of length L has a fundamental frequency f01, while a closed pipe of the
f
same length L has a fundamental frequency f02. What is the ratio of 01 ?
f 02
C A. 1: 2 B. 1: 3 C. 2: 1 D. 3: 1

U2k16-14 As shown in Fig.U2k16-14, a tuning fork of frequency 1480 Hz is placed

above the open end of the resonance tube. If the shortest length of air
column for resonance is 5.9 cm, what is the velocity of the sound in air?
C A. 335.3 m s–1 B. 341.8 m s–1
–1
C. 349.3 m s D. 355.6 m s–1
Fig.U2k16-14

Prepared by UCSCAM Resonance

Arranged by TAGoh, SYOh, JMTsu, SJChew Copyright
 13
U2k16-P9 Fig.U2k16-P9 shows a fine string passing over a fixed
frictionless pulley B, with its end A connected to an A a
B
oscillator, and the other end hanging a weight of 40 N.
The distance AB is fixed at 0.8 m and the mass per unit b
–1 oscillator
length of the string is 25 g m . When the oscillator 40 N
produces a complete vibration, a sinusoidal pulse is
produced on the string. Fig.U2k16-P8b
(a) Find the velocity of the sinusoidal pulse on the string;
(b) If the sinusoidal pulse is reflected at B, draw the corresponding reflected pulse on the string;
(c) Calculate the lowest frequency of the musical note that the string can produce;
(d) What are the frequencies that would produce stationary waves on the string when the
frequency of the oscillator is varies from 20 Hz to 120 Hz?
(e) Draw the waveform of the stationary wave on the string when the oscillator vibrates with a
frequency of 100 Hz.
[40 m s–1; 25 Hz; 25 Hz, 50 Hz, 75 Hz, 100 Hz; 4 loops stationary waves]

U2k18-P4 One of the strings of a guitar has an effective length

of 65 cm, as shown in Fig.U2k18-P4. The
fundamental frequency of the string is 110 Hz.
(a) Determine the speed of the wave on the string.
(b) Write down the frequencies of the first two harmonics
produced by the string.
(c) If the guitarist wishes to play a fundamental note of
frequency 150 Hz on the string, at what distance from
the nut must his finger press? Fig.U2k18-P4
[143 m s–1; 110 Hz, 220 Hz, 330 Hz; 0.17 m]

Prepared by UCSCAM Resonance

Arranged by TAGoh, SYOh, JMTsu, SJChew Copyright