WAVES OBJECTIVE QUESTION
Q.1 A transverse
wave is described by y= y0sin 2p (ft - xl), the maximum
particle velocity is equal to four times the wave velocity if.
(a) l = py0/4 (b) l = py0/2 (c) l = py0 (d) l = 2py0
Q.2 A wave equation
which gives the displacement along the y-direction is given by y = 10-4
sin (60t +2x), where x and y are in metres and t is in seconds. This represents
a wave
(a)
traveling with a velocity
of 30 m/s in the negative x-direction
(b)
of wavelength p meters (c) of frequency 30/p hertz
(d) of amplitude 104 metre traveling along
the negative x-direction
Q.3 A
wave is represented by the equation
Y = A sin (10 px + 15 pt + p/3)
where
is in metres and t is in seconds. The expression represents
(a)
a wave traveling in the positive x-direction with a
velocity 1.5 m/s
(b)
a wave traveling in the negative x-direction with a
velocity 1.5 m/s
(c)
a wave traveling in the negative x-direction having a
wavelength 0.2 m
(d)
a wave traveling in the positive x-direction having a
wavelength 0.2 m
Q.4 Which
of the following equations does not represent a progressive wave ?
(a) y = A sin k (x + nt) (b) y = ¦ (x - nt)
(c) y = a log (x - nt) (d) y = ¦ (x2 - n2t3)
Q.5 The displacement of a particle in a string
stretched in x-direction is represented by y. Among the following expressions
for y, those describing wave motions are
(a) cos k x sin wt (b) k2 x2 - w2 t2
(c) cos2 (kx + wt) (d) cos (k2 x2 - w2 t2)
Q.6 A bumb with the equation y = 2 ´ 10-3
e(x-4t)2 is traveling on a string 1m long, where distances are in metres
and time in seconds. If the tension in the string is 16 N, the mass of the
string is
(a) 1.6 g (b) 4.0 g (c) 10 g (d) 16 g
Q.7 Out of the following, the equation for a
cylindrical progressive wave is
(a) y = A sin wt (b) y = a/Öx sin (wt – kx)
(c) y = A sin (wt - kx) (d) y = a/x sin (wt – kx)
Q.8 Of the following the equation of a
spherical progressive wave is
(a) y = A sin wt (b) y = A sin (wt – kr)
(c) y = A/r sin (wt - kr) (d) y = A/Ör sin (wt – kr)
Q.9 A sound wave has frequency of 550 Hz,
velocity of 330 m/s and amplitude of 0.1 mm.
(a)
The distance between two points having a phase difference
of 60° is 0.1 m.
(b)
The phase difference between two points separated by a
distance of 0.3 m is p/2.
(c)
The maximum particle velocity is 0.11 p m/s.
(d)
The minimum particle velocity is zero.
Q.10 A
sinusoidal wave is traveling in a medium. Then
(a)
the minimum distance between two particles having the same
speed is l/2
(b)
the minimum distance between two particles in the same
phase is l.
(c)
the phase difference between two particles separated by a
distance of 5l/4 along the
direction of propagation of wave is p/4.
(d)
If its equation is 0.02 sin (5t – 0.2 x), the maximum
particle velocity is 0.1 m/s.
Q.11 Two
waves are represented by
y1
= sin 5 sin 2p (75 t – 0.25 x)
y2
= 10 sin 2p (150 t – 0.50
x)
The
intensity ration I1/I2 of the two waves is
(a) 1 : 2 (b) 1 : 4 (c) 1 : 8 (d) 1 : 16
Q.12 An
intensity level of zero decibel corresponds to sound wave of intensity in W/m2
to
(a) zero (b) 10 (c) 10-12 (d) 10-16
Q.13 In an observer moves twice the distance away
from a point source of sound, the intensity level falls by
(a) 2 dB (b) 3 dB (c) 4 dB (d) 6 dB
Q.14 If we turn off one of the speakers of a
stereo system, the intensity change in dB is
(a) 0.5 (b) 2.0 (c) 3 (d) 4
Q.15 Sound waves whose intensities exceed 1 W/m2
cause damage to human ears. This corresponds in dB to
(a) 1 (b) 1.2 (c) 12 (d) 120
Q.16 If two waves of the same frequency and same
amplitude superpose and produce a disturbance having the same amplitude as that
of any one of the component waves, the two waves differ in the phase by
(a) p (b) 2p/3 (c) p/2 (d) 0
Q.17 Due to arrival of four waves, a particle has
following displacements simultaneously at a certain instant
y1
= 5 sin 314 t y3
= 5 sin (314 t - p)
y2 =
5 sin (314t -2p) y4 = 5 sin (314t -3p/2)
The amplitude of
the resultant wave is
(a) 0 (b) 5 (c) 5Ö2 (d) 10
Q.18 If the ratio of maximum to minimum intensity
in an interference pattern is 49 : 1 then, the ration between amplitudes of two
interfering waves is
(a) 6 : 1 (b) 37 : 35 (c) 1 : 6 (d) 4 : 3
Q.19 Two waves of intensities I and 4 I produce
interference. The intensity constructive and destructive interference
respectively is
(a) 3 I, 5 I (b) 5I, 3 I (c) I, 9 I (d) 9 I, I
Q.20 Two waves of the same frequency produce
interference. They have amplitudes in the ratio of 1 : 3. The intensity of the
first wave is I, then
(a)
the intensity at the constructive interference is 16 I
(b)
the intensity at the destructive interference is 4 I
(c)
the intensity at the destructive interference is zero
(d)
the ratio of Imax / Imin is 4
Q.21 Beats
are produced die to superposition of two vibrations
y1
= 4 sin 400 pt
y2
= 3 sin 404 pt
situated very
near to the ears of a person. The person hears
(a)
2 beats/second with intensity ratio 4/3 between maxima and
minima
(b)
2 beats/second with intensity ratio 49/1 between maxima and
minima
(c)
4 beats/second with intensity ratio 7/2 between maxima and
minima
(d)
4 beats/second with intensity ratio 4/3 between maxima and
minima
Q.22 50 tuning forks are so arranged in series
that each fork give 5 beats per second with the previous one. If the last fork gives
the octave of the first, the frequency of the later is
(a) 245 Hz (b) 250 Hz (c) 240 Hz (d) 260 Hz
Q.23 A tuning fork of frequency 90 Hz is sounded
and moved towards an observer with a velocity equal to one-tenth the velocity
of sound. The note heard by the observer will have a frequency in Hz
(a) 100 (b) 90 (c) 80 (d) 95
Q.24 An engine is moving on a circular path of
radius 100 m with a speed of 20 m/s. What will be the frequency observed by an
observer standing stationary at the center of the circular path when the engine
blows whistle of frequency 500 Hz. (Speed of sound 340 m/s)
(a) 510 Hz (b) 500 Hz (c) 490 Hz (d) 480 Hz
Q.25 If the frequency of a note emitted by a
source changes by 20% as it approaches an observer. As it recedes away from
him, the apparent frequency
(a) 20% (b) 17.4 % (c) 16.67 % (d) 14.3 %
Q.26 The wavelength of light received from a
galaxy is 4% greater than that received from an identical source of the earth.
The velocity of the galaxy relative to the earth is
(a) 7 ´ 106 m/s (b) 12 ´ 106 m/s
(c) 0.75 ´ 106 m/s (d) 1.33 ´ 106 m/s
Q.27 A sharp tap is made by an observer standing
in front of stairs, the width of whose tread is 25.0 cm. If the velocity of
sound is 330 m/s the frequency of the note heard by him in Hz is
(a) 1320 (b) 660 (c) 445 (d) 990
Q.28 The equation of
a stationary wave on a stretched wire is
Y= 8sin px/45 sin 30pt.
Where
all distance are in cm and time in seconds
(a) The distance between two nodes is 45cm.
(b) The maximum amplitude of vibration is
8cm.
(c) Two particle on the two sides of a note
vibrate with a phase difference of p/2.
(d) All particles vibrate with the same
frequency of 15Hz.
Q.29 A wave
represented by the equation y = a cos (km-wt) is superposed with another wave to from stationary wave
such that the point x = 0 is node. The equation for the other wave is
(a) a
sin (kx+wt) (b) -a cos (kx-wt)
(c) -a
cos (kx+wt) (d) cos (k2 x2 + w2 t2)
Q.30 The displacement
of a particles in a string in the x-direction is represented by y. Among the
following expression for y, those describing wave motion are.
(a) cos kx
sinwt (b) cos2(kx + wt)
(c) k2x2- w2t2 (d) cos (k2x2- w2t2)
Q.31 A wave described
by y = A cos (wt- kt +f) is totally
reflected from a fixed end. After reflection which may change,
(a) f (b) w (c) f and w (d) k
Q.32 The displacement
y of a particle executing periodic motion is given by
Y=4 cos2 [½t] sin (1000t)
This expression may be considered to be
a result of the superposition of
(a) two (b) three (c) four (d) five
Q.33 A stretched
string of length L fixed at its ends
can sustain stationary waves of wavelength l given by
(a) l=2lL (b) l = 2L/n (c) l = L/n (d) l = Ln2
Q.34 The vibrations
of a stretched string fixed at both ends are described by y = 4sin 2px cos wt. The minimum length of the wire will be
(a) 1m (b) 0.5m (c) 5m (d) 2pm
Q.35 Two identical
straight wires are stretched so as to produce 6 beats per second when vibrating
Simultaneously. On changing the tension slightly in one of them, the beat
frequency remains unchanged. Denoting by T1,
T2 the higher and the
lower initial tensions in he strings, then it could be said that while making
the above changes in tension.
(a) T2
was decreased (b) T2
was increased
(c) T1
was increased (d) T1
was decreased
Q.36 An air column in
a pipe, which is closed at one end, will be in resonance with a tuning fork of
frequency 264Hz if the length of the column (in cm) is
(a) 31.25 (b) 62.50 (c) 93.75 (d) 125
Q.37 A tube, closed
at one end and containing air, produces, when excited, the fundamental note of
frequency 512Hz. If the tube is open at both ends the fundamental frequency
that can be excited is
(a) 1024Hz (b) 512Hz (c) 256Hz (d) 128Hz
Q.38 An organ pipe P1 closed at one end
vibrating with its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are
in resonance with a giving tuning fork. The ratio of the length of P1 to P2 is
(a) 8/3 (b) 3/8 (c) ½ (d) 1/6
Q.39 Velocity of
sound in air is 320 m/s. A pipe closed at one end has length 1m. Neglecting end
corrections, the air column in the pipe can resonate for sound of frequency:
(a) 80Hz (b) 240Hz (c) 320Hz (d) 400Hz
Q.40 An air column
closed at one end is vibrating in its fifth harmonic. If the frequency of this
harmonic wave were n times the
fundamental note emitted by air in the same tube when opened at both ends, n would be equal to
(a) 2.5 (b) 3.0 (c) 4.5 (d) 5.0
Q.41 A cylindrical
tube, open at both ends has as fundamental frequency f in air. The tube is dipped vertically in water so that half of it
is in water. The fundamental frequency of air column is now
(a) f/2 (b) 3f/4 (c) f (d) 2f
Q.42 The end
correction of a resonance column is 1.0cm. If the shortest length resonating
with a tuning fork is 15.0 cm, the next resonating length is
(a) 31cm (b) 45cm (c) 46cm (d) 47cm
Q.43 A closed organ
pipe and an open organ pipe have their first overtones identical in frequency,
their lengths are in the ratio
(a) 1:2 (b) 2:3 (c) 3:4 (d) 4:5
Q.44 In a certain
organ pipe three successive resonance frequencies ate at 425, 595 and 765 Hz.
If the speed of sound in air is 340m/s, the length of the pipe is
(a) 2m (b) 1m (c) 1.5m (d) 2.m
Q.45 A tuning fork
and a sonometer wire emitting its fundamental note gives 5 beats per seconds
both when the length of the wire is 1m or 1.05m. The velocity of transverse
wave in the sonometer wire is
(a) 420
m/s (b) 400m/s (c) 210m/s (d) 200m/s
ANSWER SHEET
1.
|
(b)
|
2.
|
(a),(b), (c), (d)
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3.
|
(b), (c)
|
4.
|
(c), (d)
|
5.
|
(a), (c)
|
6.
|
(c)
|
7.
|
(b)
|
8.
|
(c)
|
9.
|
(a), (c), (d)
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10.
|
(a), (b), (d)
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11.
|
(d)
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12.
|
(c)
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13.
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(d)
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14.
|
(c)
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15.
|
(d)
|
16.
|
(b)
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17.
|
(c)
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18.
|
(d)
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19.
|
(d)
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20.
|
(a), (b), (d)
|
21.
|
(b)
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22.
|
(a)
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23.
|
(a)
|
24
|
(b)
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25.
|
(d)
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26.
|
(b)
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27.
|
(b)
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28.
|
(a), (b), (d)
|
29.
|
(c)
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30.
|
(a), (b)
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31.
|
(a)
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32.
|
(b)
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33.
|
(b)
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34.
|
(b)
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35.
|
(b), (d)
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36.
|
(a), (c)
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37.
|
(a)
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38.
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(d)
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39.
|
(a), (b), (d)
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40.
|
(a)
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41.
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(c)
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42.
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(d)
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43.
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(c)
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44.
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(b)
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45.
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(c)
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