The document contains 8 multiple choice questions about wave properties and behaviors including: - The conditions required for two progressive waves to produce a stationary wave - Characteristics of displacement nodes in a stationary wave - Formulas for calculating frequencies of air columns vibrating in tubes at different overtones - Directions of particle motion in a transverse wave - Determining unknown frequencies using beat frequencies - Calculating string tensions and resonant frequencies in standing wave examples - Using resonance to determine unknowns like sound velocity and mass distributions

1. 1. A stationary wave is produced by the superposition of two
progressive waves.
Consider the following statements about the two
progressive waves.
These two waves should have:
a) Equal frequencies
b) Equal or approximately equal amplitudes
c) Same progressive directions
The false statement(s) is/are,
i. Only a
ii. Only b
iii. Only c
iv. Only a and b
v. Only a and c
2. Consider the displacement nodes that occur when a
stationary wave is made on some media.
a) The distance between any two displacements is equal
to the wave length of the wave.
b) Pressure node is the same as a displacement node
irrespective of the wave subjected for transmission
c) Displacement nodes vibrate with a minimum velocity.

2. The correct statement(s) is/are,
i. Only a
ii. Only b
iii. Both a and b
iv. Both a and c
v. Only c
3. An air column inside a tube of length L is vibrating in the
nth
overtone. If the velocity of sound is V, then the
frequency at which the air column is vibrating is,
i. nV/2L
ii. nV/8L
iii. (n+1)V/4L
iv. (n+1)V/2L
v. (n+2)V/2L
4. The length of a tube closed at one end is 0.2m. Assuming
that the velocity of air is 340ms-1
, the minimum
frequencies (in Hz) at which air can vibrate inside the tube
are,
i. 900, 1800, 2700
ii. 900, 1800, 5400
iii. 450, 900, 1800

3. iv. 425, 850, 1275
v. 900, 1325, 1800
5. The diagram below shows a transverse wave travelling
from left to right.
The directions of particles corresponding to points P, Q,
and R are respectively,
P Q R
(i)
(ii)
(iii)
(iv)
(v)

4. 6. When two tuning folks x and y are vibrated together the
beat frequency is 4Hz. When grease is applied to y the
beat frequency decreased to 2Hz. If the x’s frequency in
the first instance is 256Hz, y’s corresponding initial
frequency is
i. 264 Hz
ii. 258 Hz
iii. 254 Hz
iv. 260 Hz
v. 252 Hz
7. A string tied at one end to a rigid wall and the other end to
a load is shown below.
P
Q R

5. First the AB part of the string is vibrated at a constant
frequency. When a tuning folk frequency of 256 Hz was
kept near the vibrating string the beat frequency was 4 Hz.
Assume that the tension of the string at this instance is T1 .
Then the load Mg is changed until the tension of the string
is changed to T2. When a tuning folk of frequency 128Hz
was kept near the vibrating string the beat frequency was
2Hz.Assume that at both instances the frequencies of the
tuning folks is greater than the frequencies at which the
string is vibrating.
What is the ratio of T1 / T2 ?
8. An 80 cm long one end opened pipe is vibrated by its 2nd
overtone. Simultaneously a x m long both ends opened
pipe (length can be changed as needed) is vibrated by its
3rd
overtone.
BA
C
Mg

6. After these vibrations are completed, a tuning folk of
frequency 256 Hz is made to vibrate with the air column of
the both ends opened tube. It was noticed that the beat
frequency dropped as the length of the tube was increased
and resonance occurred at some length of the tube while
adjusting its length.
If resonance occurred when the one end closed pipe was
made to vibrate with a vibrating source of frequency 530
Hz, calculate x and the velocity of sound in air.
Finally, length of the both ends opened pipe was doubled
and another 3rd
overtone was obtained. Here the pie was
made to resonate with an apparatus as shown below
(consider that the length of AB (0.75 m) was made to
resonate and that the string is light and inelastic).
Assuming g = 10ms-2
, calculate the mass per unit length of
the string.
M kg
A B
0.75 m

7. Answers:
1. 3
2. 5
3. 4
4. 4
5. 4
6. 4
7. 2
8. 2.6m, 340ms-1
, 2 × 10-4
kgm-1