iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 25th July Evening Shift
Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt3$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 25th July Morning Shift
An observer is riding on a bicycle and moving towards a hill at $18 \,\mathrm{kmh}^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $640 \mathrm{~Hz}$ and velocity of the sound in air is $320 \mathrm{~m} / \mathrm{s}$, the beat frequency between the two sounds heard by observer will be _____________ $\mathrm{Hz}$.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 30th June Morning Shift
An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh$-$1 in the direction of wind which is blowing at 72 kmh$-$1 speed. Frequency of siren is 720 Hz. The employee hears an apparent frequency of ____________ Hz.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 29th June Evening Shift
In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms$-$1. The third resonance is observed when the air column has a length of _____________ cm.
Correct Answer: 104
Explanation:
$400 = {v \over {4({L_1} + e)}}$ ..... (i)
$400 = {{5v} \over {4({L_2} + e)}}$ ..... (ii)
$ \Rightarrow {L_1} + e = {\lambda \over 4} = 21$ cm
${L_2} + e = {{5\lambda } \over 4} = 105$ cm
$\Rightarrow$ e = 1 cm & L2 = 104 cm
2022
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 28th June Evening Shift
A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ___________ cm.
(Velocity of sound in air is 340 ms$-$1)
Correct Answer: 50
Explanation:
Given $340 = {n \over {4 \times 125}}v$
$ \Rightarrow n = 5$
So $\lambda = 100$ cm
So minimum height is ${\lambda \over 2} = 50$ cm
2022
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 26th June Evening Shift
A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.
Correct Answer: 152
Explanation:
Given ${v_{20}} = 2{v_1}$
Also ${v_{20}} = 4 \times 19 + {v_1}$
So ${v_{20}} = 152\,Hz$
2022
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 25th June Morning Shift
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is _____________ cm.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 24th June Evening Shift
Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $y = (10\cos \pi x\sin {{2\pi t} \over T})$ cm
The amplitude of the particle at $x = {4 \over 3}$ cm will be ___________ cm.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 26th July Evening Shift
A transverse wave is represented by $y=2 \sin (\omega t-k x)\, \mathrm{cm}$. The value of wavelength (in $\mathrm{cm}$) for which the wave velocity becomes equal to the maximum particle velocity, will be :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 30th June Morning Shift
Which of the following equations correctly represents a travelling wave having wavelength $\lambda$ = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 29th June Morning Shift
A longitudinal wave is represented by $x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$ cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 27th June Evening Shift
If a wave gets refracted into a denser medium, then which of the following is true?
A.
wavelength, speed and frequency decreases.
B.
wavelength increases, sped decreases and frequency remains constant.
C.
wavelength and speed decreases but frequency remains constant.
D.
wavelength, speed and frequency increases.
Correct Answer: C
Explanation:
Frequency is independent of medium. For denser medium, wavelength and speed both would decrease.
2022
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 27th June Morning Shift
An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 31st August Morning Shift
A wire having a linear mass density 9.0 $\times$ 10$-$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ____________ m.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th August Evening Shift
A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be __________ cm. (Take speed of sound in air as 340 ms$-$1)
Correct Answer: 34
Explanation:
${\lambda \over 4}$ = l $\Rightarrow$ $\lambda$ = 4l
f = ${V \over \lambda } = {V \over {4l}}$
$\Rightarrow$ 250 = ${{340} \over {4l}}$
$\Rightarrow$ l = ${{34} \over {4 \times 25}}$ = 0.34 m
l = 34 cm
2021
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th August Morning Shift
Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is .................. Hz.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th August Evening Shift
Two waves are simultaneously passing through a string and their equations are :
y1 = A1 sin k(x $-$ vt), y2 = A2 sin k(x $-$ vt + x0). Given amplitudes A1 = 12 mm and A2 = 5 mm, x0 = 3.5 cm and wave number k = 6.28 cm$-$1. The amplitude of resulting wave will be ................ mm.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th August Morning Shift
A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be ............... Hz.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th August Morning Shift
Two travelling waves produces a standing wave represented by equation,
y = 1.0 mm cos(1.57 cm$-$1) x sin(78.5 s$-$1)t.
The node closest to the origin in the region x > 0 will be at x = .............. cm.
Correct Answer: 1
Explanation:
For node
cos(1.57 cm$-$1)x = 0
(1.57 cm$-$1)x = ${\pi \over 2}$
x = ${\pi \over {2(1.57)}}$ cm = 1 cm
2021
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 20th July Morning Shift
The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ___________ km/h.
$ \Rightarrow 9v = 330 \Rightarrow v = {{330} \over 9}$ m/s
or $v = {{330} \over 9} \times {{18} \over 5} = 132$ km/h
2021
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 20th July Morning Shift
The amplitude of wave disturbance propagating in the positive x-direction is given by $y = {1 \over {{{(1 + x)}^2}}}$ at time t = 0 and $y = {1 \over {1 + {{(x - 2)}^2}}}$ at t = 1 s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___________ m/s.
Correct Answer: 2
Explanation:
As per question,
at t = 0, y = ${1 \over {{{(1 + x)}^2}}}$
and at t = 1 s, y = ${1 \over {1 + {{(x - 2)}^2}}}$ .... (i)
As we know,
At t = t s, y = ${1 \over {1 + {{(x - vt)}^2}}}$
So, at t = 1 s, y = ${1 \over {1 + {{(x - v)}^2}}}$ .... (ii)
On comparing Eqs. (i) and (ii), we get
v = 2 ms$-$1
Hence, the velocity of the wave will be 2 m/s.
2021
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 16th March Evening Shift
A closed organ pipe of length L and an open organ pipe contain gases of densities $\rho$1 and $\rho$2 respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is ${x \over 3}L\sqrt {{{{\rho _1}} \over {{\rho _2}}}} $ where x is ___________. (Round off to the Nearest Integer)
Correct Answer: 4
Explanation:
First overtone of open pipe $ = {{{v_2}} \over {{L_2}}}$
First overtone of closed pipe at one end $ = {{3v} \over {4L}}$
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th February Morning Shift
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $-$ 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x $\times$ 10$-$2 N. Value of x is _________. (Round off to the nearest integer)
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 24th February Evening Shift
Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ___________ Hz. [Velocity of sound in air is 340 m/s.]
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 22th July Evening Shift
The motion of a mass on a spring, with spring constant K is as shown in figure.
The equation of motion is given by x(t) = A sin$\omega$t + B cos$\omega$t with $\omega$ = $\sqrt {{K \over m}} $
Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos($\omega$t $-$ $\phi$), where C and $\phi$ are :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 17th March Evening Shift
A sound wave of frequency 245 Hz travels with the speed of 300 ms$-$1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th February Evening Shift
A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?
A.
335 Hz
B.
345 Hz
C.
338 Hz
D.
342 Hz
Correct Answer: A
Explanation:
Initially beat frequency = 5Hz
so, $\rho$A = 340 $ \pm $ 5 = 345 Hz, or 335 Hz
after filing frequency increases slightly so, new value of frequency of A > $\rho$A
Now, beat frequency = 2Hz
$ \Rightarrow $ new $\rho$A = 340 $ \pm $ 2 = 342 Hz, or 338 Hz
hence, original frequency of A is $\rho$A = 335 Hz
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 25th February Morning Shift
A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is :
A.
13 cm
B.
18.4 cm
C.
16.6 cm
D.
14.8 cm
Correct Answer: D
Explanation:
$ \therefore $ $l + 1.8 = {\lambda \over 4}$
Also $\lambda = {v \over f} = {{336} \over {504}}$
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 24th February Evening Shift
Which of the following equations represents a travelling wave?
A.
y = Aexcos($\omega$t $-$ $\theta$)
B.
y = Ae$-$x2(vt + $\theta$)
C.
y = A sin (15x $-$ 2t)
D.
y = A sinx cos$\omega$t
Correct Answer: C
Explanation:
Y = F(x, t)
For travelling wave y should be linear function of x and t and they must exist as (x $\pm$ vt)
Y = A sin (15x $-$ 2t) $ \to $ linear function in x and t.
2020
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 8th January Morning Slot
A one metre long (both ends open) organ pipe
is kept in a gas that has double the density of
air at STP. Assuming the speed of sound in air
at STP is 300 m/s, the frequency difference
between the fundamental and second harmonic
of this pipe is ________ Hz.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 6th September Morning Slot
A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency
v0
(see figure). An observer is standing at a finite distance, at the point O, from the track. The
time variation of frequency heard by the observer is best represented by: (t0
represents the
instant when the distance between the source and observer is minimum)
When source is approaching towards observer then $\theta $ is inceasing so cos$\theta $ is decreasing. As cos$\theta $ is decreasing so c - vcos$\theta $ is increasing. Then v will decrease.
When source is receding from observer then $\theta $ is decreasing so cos$\theta $ is increasing. As cos$\theta $ is increasing so c + vcos$\theta $ is increasing. Then v will also decrease.
As v is changing depending on cos$\theta $, so curve should look like cos$\theta $ curve.
2020
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 5th September Evening Slot
A driver in a car, approaching a vertical wall
notices that the frequency of his car horn, has
changed from 440 Hz to 480 Hz, when it gets
reflected from the wall. If the speed of sound in
air is 345 m/s, then the speed of the car is :
A.
36 km/hr
B.
54 km/hr
C.
24 km/hr
D.
18 km/hr
Correct Answer: B
Explanation:
f1 = frequency heard by wall
= $\left( {{{{v_s} - 0} \over {{v_s} - {v_c}}}} \right){f_0}$ = ${{{{v_s}} \over {{v_s} - {v_c}}} \times 440}$
f2 = frequency heard by driver after reflection from wall
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 5th September Morning Slot
Assume that the displacement(s) of air is
proportional to the pressure difference ($\Delta $p)
created by a sound wave. Displacement (s)
further depends on the speed of sound (v),
density of air ($\rho $) and the frequency (f). If
$\Delta $p ~ 10 Pa, v ~ 300 m/s, $\rho $ ~ 1 kg/m3 and f ~ 1000 Hz,
then s will be of the order of (take the
multiplicative constant to be 1) :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 5th September Morning Slot
In a resonance tube experiment when the tube
is filled with water up to a height of 17.0 cm
from bottom, it resonates with a given tuning
fork. When the water level is raised the next
resonance with the same tuning fork occurs at
a height of 24.5 cm. If the velocity of sound in
air is 330 m/s, the tuning fork frequency is :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 4th September Evening Slot
The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes
from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the
bus if speed of the sound is 330 ms–1.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 4th September Morning Slot
For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the are :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 3rd September Morning Slot
A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is
produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it
reaches the top of the rope ?
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 2nd September Morning Slot
Two identical strings X and Z made of same
material have tension TX and TZ in them. If their
fundamental frequencies are 450 Hz and
300 Hz, respectively, then the ratio TX/TZ is
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 9th January Evening Slot
A wire of length L and mass per unit length
6.0 × 10–3 kgm–1 is put under tension of
540 N. Two consecutive frequencies that it
resonates at are : 420 Hz and 490 Hz. Then L
in meters is :
A.
5.1 m
B.
2.1 m
C.
1.1 m
D.
8.1 m
Correct Answer: B
Explanation:
Fundamental frequency = 70 Hz.
70 = ${1 \over {2l}}\sqrt {{T \over \mu }} $
$ \Rightarrow $ $l$ = 2.14 m
2020
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 9th January Morning Slot
Three harmonic waves having equal frequency
$\nu $ and same intensity ${I_0}$, have phase angles 0, ${\pi \over 4}$ and $ - {\pi \over 4}$ respectively. When they are
superimposed the intensity of the resultant wave
is close to :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 8th January Evening Slot
A transverse wave travels on a taut steel wire
with a velocity of v when tension in it is
2.06 × 104 N. When the tension is changed to
T, the velocity changed to v/2. The value of T
is close to :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 7th January Evening Slot
A stationary observer receives sound from two identical tuning forks, one of which approaches
and the other one recedes with the same speed (much less than the speed of sound). The
observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v0
= 1400 Hz and the
velocity of sound in air is 350 m/s. The speed of each tuning fork is close to :
$ \Rightarrow $ v = ${{350} \over {1400}}$ = ${1 \over 4}$ m/s
2020
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2020 (Online) 7th January Morning Slot
Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 $ \times $ 1011 Nm-2, the extension of wire over its natural length is :
A.
0.03 mm
B.
0.04 mm
C.
0.02 mm
D.
0.01 mm
Correct Answer: A
Explanation:
Velocity of the wave, v = $\sqrt {{T \over \mu }} $
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2019 (Online) 12th April Evening Slot
Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from
source S1 towards S2 with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s.
Then, u equals :
A.
10.0 m/s
B.
5.5 m/s
C.
15.0 m/s
D.
2.5 m/s
Correct Answer: D
Explanation:
As observer goes away from source S1 so apparent frequency,
${f_1} = \left( {{{v - u} \over v}} \right)f$
here $v$ = speed of sound, $u$ = speed of observer
As observer goes towards source S2 so apparent frequency,
${f_2} = \left( {{{v + u} \over v}} \right)f$
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2019 (Online) 12th April Evening Slot
A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air
by resonance tube method. Resonance is observed to occur at two successive lengths of the air column,
l1 = 30 cm and l2 = 70 cm. Then, v is equal to -
A.
338 ms–1
B.
384 ms–1
C.
379 ms–1
D.
332 ms–1
Correct Answer: B
Explanation:
We know,
$\lambda $ = 2(${l_2} - {l_1}$)
given ${l_2}$ = 70 cm and ${l_1}$ = 30 cm
$ \therefore $ $\lambda $ = 2(70 - 30) = 80 cm
Also we know, v = $\lambda $$f$ = 0.8 $ \times $ 480 = 384 m/s
2019
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2019 (Online) 12th April Evening Slot
A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB
intensity sound ? [Given reference intensity of sound as 10–12 W/m2
]
