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A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. .K the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end ?
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A stone dropped from the top of a tower of height 300 m
high splashes into the water of a pond near the base of the tower. When is the
splash heard at the top ? Given that the speed of sound in air is
-
A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound m dry air at 20°C = 343
.
-
Use the formula
to
explain why the speed of sound in
air
(a) is independent of pressure, (b) increases with
temperature, (c) increases with humidity.
-
You have learnt that a travelling wave in one dimension is
represented by a function y =f(x, t), j where x and (must appear in the
combination (x -
t) or
(x +
t), i.e., y =f
(x ±
t). Is the
converse y true ? That is, does every function of (x -
t) or (x +
t) represent a
travelling wave ? Examine, if ^ the following functions for y can possibly
represent a travelling wave ? "^
(a)
(b)
(c)
-
A bat emits ultrasonic sound of frequency 100 k Hz in air.
If this sound meets a water surface, what is the wavelength of (a) the
reflected sound (b) the transmitted sound ? Speed of sound in air = 340
and in water =
1486
.
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A hospital uses ah ultrasonic scanner to locate tumours in a
tissue. What is the wavelength of sound m a tissue in which the speed of sound
is
The operating
frequency of the scanner is
MHz.
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A transverse harmonic wave on a string is
described by y (x, t) = 3.0 sin (36t + 0.018 x +
/4), where x, y
are m cm and t in sec. The positive direction of x-axis is from left to right.
(i)
Is this a travelling or a stationary wave ? If it is travelling, what are the
speed and direction of its propagation ? (ii) what are its amplitude and
frequency ? (iii) what is the initial phase at the origin ? (iv) What is the
least distance between two successive crests in the wave ?
-
For the wave described in Q.8 above, plot the displacement
(y) versus (t) graphs for x=0, 2 and 4 cm. What are the shapes of these graphs
? In which aspects dose the oscillatory motion in travelling wave differ from
one point to another : amplitude, frequency or phase ?
-
For the travelling harmonic wave, y (x, t) = 2.0 cos 2 n
[10t ? 0.0080 x + 0.35], where x and y are in cm and t in s, what is the phase
difference between oscillatory motion at two points separated by a distance of
(i) 4 m (ii) 0-5 m (iii)
/2
(iv) 3
/4 ?
-
The transverse displacement of a string (clamped at its two
ends) is given by
where
x, y are m m and t in s. The length of the string is 1.5 m and its mass is 3 x
kg. Answer the following:
(i)
Does the function represent a travelling or a stationary wave
?
(ii)
Interpret the wave as a superimposition of two waves travelling in opposite directions.
What are the wavelength, frequency and speed of propagation of each wave
?
(iii) Determine the tension in the
string.
-
(i) For the wave on a string described in Q. 11 above, do all the points on the string osculate with the same (a) frequency, (b) phase, (c) amplitude ? Explain your answers, (ii) What is the amplitude of a point 0.375 m away from one end ?
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Given below are some functions of x and t to represent the
displacement (transverse or longitudinal) of an elastic wave. State which of
these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at
all?
(a)
(b)
(c)
(d)
-
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is
and its linear mass density is
What is (a) the speed of a transverse wave on the string, and (b) the tension in the string ?
-
A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment The edge effects may be neglected.
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A steel rod 100 cm long is clamped at its middle. The
fundamental frequency of longitudinal vibrations of the rod is given to be 2.53
k Hz. What is the speed of sound in steel ?
-
A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source ? Will this source be in resonance with the pipe, if both ends are open. Speed of sound = 340 m/s.
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Two sitar strings A and ? playing the note 'Ga' are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?
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Explain why (or how): (a) In a sound wave, a displacement node is a pressure antinode and vice-versa,
(b) Bats can ascertain distances, directions, nature and size of obstacles without any eyes,
(c) a violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,
(d) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases,
(e) The shape of pulse gets distorted during propagation in a dispersive medium.
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A train, standing at the outer signal of a
railway station blows a whistle of frequency 400 Hz in still air. (i) What is
the frequency of the whistle for a platform observer when the train (a)
approaches the platform with a speed of 10
, (b) recedes
from the platform with a speed of 10
?
(ii)
What is the speed of sound in each case ? The speed of sound in still an- can
be taken as 340
.
-
A train, standing in a stationyard, blows a
whistle of frequency 400 Hz in still air. The wind starts blowing in the
direction from the yard to the station at a speed of 10
. What are the
frequency, wavelength, and speed of sound for an observer standing on the
station's platform ? Is the situation exactly identical to the case when
the air is still and the observer runs towards the yard at a speed of 10
? The speed of
sound in still air can be taken as 340
.
-
A travelling harmonic wave on a string is described by y
(x, t) = 7.5 sin (0.0050 x + 121 +
/4)
(a) what are the displacement and velocity of oscillation of a point at x = 1
cm, and ( = 1 s ? Is this velocity equal to the velocity of wave propagation ?
(b)
Locate the points of the string which have the same transverse displacement and
velocity as the x = 1 cm point at (= 2 s, 5 s and 11 s.
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A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium.
(a) Does the pulse have a definite (i) wavelength (ii) frequency (iii) speed of propagation.
(b) If the pulse rate is 1 after every 20 s, i.e. the whistle is blown for a split second after every 20 second), is the frequency of the note produced by the whistle equal to 1/20 = 0-05
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One end of a long string of linear mass density
is connected to
an electrically
driven
tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied
to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming
energy so that reflected waves at this end have negligible amplitude. At ( = 0,
the left end (fork end) of the string x = 0 has zero transverse displacement (y
= 0) and is moving along positive y-direction. The amplitude of the wave is 5.0
cm. Write down the transverse displacement (y = 0).y as function of x and t
that describes the wave on the string.
-
A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km
What is the frequency of sound reflected by the submarine ? Take the speed of sound in water to be 1450
.
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Earthquakes generate sound waves inside the earth. Unlike a
gas, the earth can experience both transverse (S) and longitudinal (P) sound
waves. Typically, the speed of S wave is about 4.0 km
,and that of P
wave is 8.0 km
. A seismograph
records P and S waves from an earthquake. The first P wave arrives 4 min before
the first S wave. Assuming the waves travel in straight line, how far away does
the earthquake occur ?
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A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in air. What frequency does the bat hear reflected off the wall?
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question_answer28)
Water
waves produced by a motor boat sailing in water are
(a)
neither longitudinal nor transverse.
(b)
both longitudinal and transverse.
(c)
only longitudinal
(d)
only transverse.
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question_answer29)
Sound waves of
wavelength \[\lambda \] travelling
in a medium with a speed of \[\upsilon \] m/s enter into another medium where its
speed is 2u m/s. Wavelength of sound waves in the second medium is
(a)
\[\lambda \] (b) \[\frac{\lambda }{2}\]
(c)
\[2\lambda \] (d) \[4\lambda \]
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question_answer30)
Speed
of sound wave in air
(a)
is independent of temperature.
(b)
increase with pressure.
(c)
increases with increase in humidity.
(d)
decreases with increase in humidity.
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question_answer31)
Change
in temperature of the medium changes
(a)
frequency of sound waves.
(b)
amplitude of sound waves.
(c)
wavelength of sound waves.
(d)
loudness of sound waves.
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question_answer32)
With
propagation of longitudinal waves through a medium, the quantity transmitted is
(a)
matter
(b)
energy
(c)
energy and matter
(d)
energy, matter and momentum
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question_answer33)
Which
of the following statements are true for wave motion?
(a)
Mechanical transverse waves can propagate through all mediums.
(b)
Longitudinal waves can propagate through solids only.
(c)
Mechanical transverse waves can propagate through solids only.
(d)
Longitudinal waves can propagate through vacuum.
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question_answer34)
A
sound wave is passing through air column in the form of compression and
rarefaction. In consecutive compressions and rarefactions.
(a)
density remains constant.
(b)
Boyle's law is obeyed.
(c)
bulk modulus of air oscillates.
(d)
there is no transfer of heat.
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question_answer35)
Equation
of a plane progressive wave is given by \[y=0.6\,\sin \,\,2\pi \left(
t-\frac{x}{2} \right)\]. On reflection from a denser medium its amplitude
becomes 2/3 of the amplitude of the incident wave. The equation of the
reflected wave is
(a)
\[y=0.6\,\sin \,\,2\pi \left( t+\frac{x}{2} \right)\]
(b)
\[y=-0.4\,\sin \,\,2\pi \left( t+\frac{x}{2} \right)\]
(c)
\[y=0.4\,\sin \,\,2\pi \left( t+\frac{x}{2} \right)\]
(d)
\[y=-0.4\,\sin \,\,2\pi \left( t-\frac{x}{2} \right)\]
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question_answer36)
A
string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string
is 20.0 m. If the transverse jerk is struck at one end of the string, the
disturbance will reach the other end in
(a)
one second
(b)
0.5 second
(c)
2 seconds
(d)
data given is insufficient.
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question_answer37)
A
train whistling at constant frequency is moving towards a station at a constant
speed V. The train goes past a stationary observer on the station. The
frequency \[n'\] of
the sound as heard by the observer is plotted as a function of time \[t\]
(Fig ).
Identify the expected curve.
(a)
(b) 
(c)
(d) 
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question_answer38)
A
transverse harmonic wave on a string is described by \[y(x,\,t)=3.0\,\sin
\,(36t+0.018x+\pi /4)\] where
\[x\] and
\[y\] are
in cm and \[t\] is
in \[s\]. The positive direction of \[x\] is from left to right.
(a)
The wave is travelling from right to left.
(b)
The speed of the wave is \[20\,\,m/s\]
(c)
Frequency of the wave is \[5.7\,Hz\]
(d)
The least distance between two successive crests in the wave is 2.5 cm.
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question_answer39)
The
displacement of a string is given by \[y\,(x,\,t)=0.06\,\sin \,(2\pi x/3)\,\cos
\,(120\,\pi t)\], where \[x\] and \[y\] are in \[m\] and \[t\] in \[s\]. The
length of the string is 1.5 in and its mass is\[3.0\times {{10}^{-2}}\,k\,g\].
(a)
It represents a progressive wave of frequency 60 Hz.
(b)
It represents a stationary wave of frequency 60 Hz.
(c)
It is the result of superposition of two waves of wavelength 3 in, frequency 60
Hz each travelling with a speed of 180 m/s in opposite direction.
(a)
Amplitude of this wave is constant.
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question_answer40)
Speed
of sound waves in a fluid depends upon
(a)
directly on density of the medium.
(b)
square of Bulk modulus of the medium.
(c)
inversely on the square root of density.
(d)
directly on the square root of bulk modulus of the medium.
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question_answer41)
During
propagation of a plane progressive mechanical wave
(a)
all the particles are vibrating in the same phase.
(b)
amplitude of all the particles is equal.
(c)
particles of the medium executes S.H.M.
(d)
wave velocity depends upon the nature of the medium.
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question_answer42)
The transverse
displacement of a string (clamped at its both ends) is given by \[y\,(x,\,t)=0.06\]\[\sin
\,(2\pi x/3)\,\cos \,(120\,\pi t)\]. All the points on the string between two
consecutive nodes vibrate with
(a)
same frequency
(b)
same phase
(c)
same energy
(d)
different amplitude.
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question_answer43)
A
train, standing in a station yard, blows a whistle of frequency 400 Hz in still
air. The wind starts blowing in the direction from the yard to the station with
a speed of 10 m/s. Given that the speed of sound in still air 340 m/s,
(a)
the frequency of sound as heard by an observer standing on the platform is 400
Hz.
(b)
the speed of sound for the observer standing on die platform is 350 m/s.
(c)
the frequency of sound as heard by the observer standing on the platform will
increase.
(d)
the frequency of sound as heard by the observer standing on the platform will
decrease.
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question_answer44)
Which
of the following statements are true for a stationary wave?
(a)
Every particle has a fixed amplitude which is different front amplitude of its
nearest particle.
(b)
All the particles cross their mean position at the same time.
(c)
All the particles are oscillating with same amplitude.
(d)
There is no net transfer of energy across any plane.
(e)
There are some particles which are always at rest.
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question_answer45)
A
sonometer wire is vibrating in resonance with a tuning fork. Keeping the
tension applied same, the length of the wire is doubled. Under what conditions
would the tuning form still be is resonance with the wire?
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question_answer46)
An organ pipe of
length L open at both ends is found to vibrate in its first harmonic when
sounded with a tuning form of 480 Hz. What should be the length of a pipe
closed at one end, so that it also vibrates in its first harmonic with the same
tuning fork?
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question_answer47)
A
tuning fork A, marked 512 Hz, produces 5 bets per second, where sounded with
another unmarked tuning fork B. If B is loaded with wax the number of beats is
again 5 per second. What is the frequency of the tuning fork B when not loaded?
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question_answer48)
The
displacement of an elastic wave is given by the function \[y=3\,\sin \,\omega
t+4\,\cos \,\omega t\]
Where
\[y\] is
in cm and t is in second. Calculate the resultant amplitude.
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question_answer49)
A
sitar wire is replaced by another wire of same length and material but of three
times the earlier radius. If the tension in the wire remains the same, by what
factor will the frequency change?
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question_answer50)
At
what temperature (in \[^{o}C\]) will the speed of sound in air be 3 times its
value of \[{{O}^{o}}C\]?
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question_answer51)
When two waves of
almost equal frequencies \[{{n}_{1}}\] and \[{{n}_{2}}\] reach at a point
simultaneously, what is the time interval between successive maxima?
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question_answer52)
A
steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed
of a transverse wave on this wire when a tension of \[2.06\times
{{10}^{4}}\,N\] is
applied?
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question_answer53)
A pipe 20 cm long
is closed at one end. Which harmonic mode of the pipe is resonantly existed by
a source of 1237.5 Hz? (sound velocity in air \[=330\,\,m\,{{s}^{-1}}\])
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question_answer54)
A
train standing at the outer signal of a railway station blows a whistle of
frequency 400 Hz still air. The train begins to move with a speed of \[10\,\,m\,{{s}^{-1}}\]
towards the
platform. What is the frequency of the sound for an observer standing on the
platform?
(sound
velocity in air \[=330\,m\,{{s}^{-1}}\])
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question_answer55)
The
wave pattern on a stretched string is shown in fig. Interpret what kind of wave
this is and find its wavelength.
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question_answer56)
The
pattern of standing waves formed on stretched string at two instants of time
are shown in fig. The Velocity of two waves superimposing to form stationary
waves is \[360\,\,m\,{{s}^{-1}}\] and their frequencies are 256 Hz. 
(a) Calculate the
time at which the second curve is plotted.
(b) Mark nodes and
antinodes on the curve.
(c) Calculate the
distance between ?A? and C?.
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question_answer57)
A
tuning fork vibrating with a frequency of 512 Hz is kept close to the open end
of a tub filled with water (Fig.). The water level in the tube is gradually
lowered. When the water level is 17 cm below die open end, maximum intensity of
sound is heard. If the room temperature is \[{{20}^{o}}C\], calculate
(a)
speed of sound in air at room temperature
(b)
speed of sound in air at \[{{0}^{o}}C\]
(c)
If die water in the tube is replaced with mercury, will there be any difference
in your observations?
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question_answer58)
Show
that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops
and 4 loops, die frequencies are in the ratio 1 : 2 : 3 : 4.
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question_answer59)
The
earth has a radius of 6400 km. The inner core of 1000 kin radius is solid.
Outside it, there is a region from 1000 km to a radius of 3500 kin which is in
molten state. Then again from 3500 kin to 6400 km die earth is solid. Only
longitudinal (P) waves can travel inside a liquid. Assume that the P wave has a
speed of \[8\,km\,{{s}^{-1}}\]in solid parts and of \[5\,km\,{{s}^{-1}}\]
in liquid
parts of the earth. An earthquake occurs at some place close to the surface of
die earth. Calculate the time after which it will be recorded in a seismometer
at a diametrically opposite point on the earth if wave travels along diameter?
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question_answer60)
If c is r.m.s.
speed of molecules in a gas and \[\upsilon \] is the speed of sound waves in the
gas, show that the gas, slow \[c/\upsilon \] constant and independent of
temperature for all diatomic gases.
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question_answer61)
Given
be low are some functions of \[x\] and \[t\] to represent to represent the
displacement of an elastic wave.
(a)
\[y=5\,\cos \,(4x)\,\sin \,(20\,t)\]
(b)
\[y=5\,\sin \,(5x=t/2)+3\cos \,(5x-t/2)\]
(c)
\[y=10\,\cos \,[(252-250\,\pi ]\]\[\cos [(252+250)\pi t]\]
(d)
\[y=100\,\cos \,(100\pi t+0.5\,x)\]
State
which of these represent
(a)
a travelling wave along \[-x\] direction
(b)
a stationary wave
(d)
a travelling wave along \[+x\] direction.
Given
reasons for your answers.
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question_answer62)
In
the given progression wave
\[y=5\sin
\,(100\,\pi t-0.4\,\pi x)\]
where
\[y\] and
\[x\] are
in \[m,\,t\] in
\[s\]. What is the
(a) Amplitude
(b) wavelength
(c) frequency
(d) Wave velocity
(e) Particle
velocity amplitude?
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question_answer63)
For
the harmonic travelling wave \[y=2\,\cos \,2\pi (10t-0.0080\,x+3.5)\]where \[x\]
and \[y\] are in cm and \[t\] is second. What is the phase difference between
the oscillatory motion at two points separated by a distance of
(a)
4 m
(b)
0.5 m
(c)
\[\frac{\lambda }{2}\]
(d)
\[\frac{3\lambda }{4}\] (at a given instant of time)
(e)
What is the phase difference between the oscillation of a particle located at\[x=100\,cm,\]at\[t=Ts\]
and\[t=5s\]
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