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1.

Two waves of wavelength 50 cm and 51 cm produce 12 beat/s . The speed of sound isA. `340 ms^(-1)`B. `332 ms^(-1)`C. `153 ms^(-1)`D. `306 ms^(-1)`

Answer» Correct Answer - D
The frequency of beats is given by
`n=n_(1)-n_(2)=v/lambda_(1)-v/lambda_(2)=v(1/0.05-1/0.51)`
`implies 12=v(2-1.9608)=v xx 0.0392`
or, `v=12/0.0392=306 ms^(-1)`
2.

After reflection from the open end a transverse progressive wave `y_1 =A sin 2pi (t//T-x//lambda ) ` travels along the direction of negative X-axis The equation of the reflected wave will beA. `y^(2) =A sin 2pi (t//T-lambda //x)`B. ` y^(2) =-A sin 2pi (t//T+x//lambda ) `C. `y_2 =A sin 2pi (t//T) +x //lambda ) `D. ` y_2=A cos 2pi (t//T- x//lambda ) `

Answer» Correct Answer - C
3.

A wave is described by the equation `y = (1.0 mm) sin pi((x)/(2.0 cm) - (t)/(0.01 s))`. (a) Find time period and wavelength. (b) Find the speed of particle at `x = 1.0 cm` and time `t = 0.01 s`. ( c ) What are the speed of the partcle at `x = 3.0 cm`, `5.0 cm and 7.0 cm` at `t = 0.01 s`? (d) What are the speeds of the partcle at `x =1.0 cm` at `t = 0.011` , `0.012 and 0.013 s`?

Answer» Correct Answer - A::B::C::D
(a) :. `T = (2pi)/(omega) = (2pi)/(pi//0.01) = 0.02 s`
`= 20ms`
`lambda = (2pi)/(k) =(2pi)/(pi//2)`
`= 4.0 cm`
(b) `v_(P) = (dely)/(delx)`
`= (-(pi)/(0.01)(mm)/(s)) cos pi((x)/(2.0 cm) -(t)/(0.01 s))`
`=( -(pi)/(10)(m)/(s)) cos pi((x)/(2.0 cm) -(t)/(0.01 s))`
Put `x= 1 cm` and `t = 0.01 s` in above equation
We get,
`v_(P) = 0`
( c ) and (d) Putting the given values in the above equation, we get the answer.
4.

A transverse wave along a string is given by `y = 2 sin (2pi (3t - x) + (pi)/(4))` where x and y are in cm and t in second. Find acceleration of a particle located at x = 4 cm at t = 1s.A. `36 sqrt(2)pi^(2) cm//s^(2)`B. `36 pi^(2) cm//s^(2)`C. `-36 sqrt(2)pi^(2)cm//s^(2)`D. `-36 pi^(2) cm//s^(2)`

Answer» Correct Answer - C
5.

Assertion :on reflection from a rigid boundary (denser medium) there is a complete reversal of phase. Reason : This is because o reflection at a denser medium. Both the particle velocity and wave velocity are reversed in sign.A. Assertion is True ,Reason is True , Reason is a correct explanation for AssertionB. Assertion is True, Reason is True , Reason is not a correct explanation for AssertionC. Assertion is True ,Reason is FalseD. Assertion is False but , Reason is True

Answer» Correct Answer - C
6.

The displacement `y` of a wave travelling in the x-direction is given by `y = 10^(-4) sin ((600t - 2x + (pi)/(3))meters` where `x` is expressed in meters and `t` in seconds. The speed of the wave-motion, in `ms^(-1)`, isA. 200B. 300C. 600D. 1200

Answer» Correct Answer - A
7.

Two engines pass each other in opposite directions with a velocity of `60 kmh^(-1)`each . One of them is emitting a note of frequency 540.Calculate the frequencies heard in the other engine before and after they have passed each other.Given velocity of sound `=316.67 ms^(-1)`.

Answer» Correct Answer - 600 Hz, 486 Hz
8.

A source is approaching towoed a wall as shown in figure .We have three observes `O_(1),O_(2) `and `O_(3). observer `O_(2) is over the source itself . Let `f_(1),f_(2)and `f_(3) be the beat frequencires heard by `O_(1),O_(2) `and `O_(3)` between direct sound from the source and reflected sound from the wall . then A. (a)`f_(3)=0B. `f_(1)gt f_(2)`C. both(a) and (b) are wrongD. both (a) and (b) are correct

Answer» Correct Answer - D
9.

Two sound waves trevelling in same direction can be represented as `y_(1)=(0.02 mm)sin [(400 pi rad s^(-1))(x/(330 ms^(-1))-t)]` And `y_(2)=(0.02 mm)sin [(404 pi rad s^(-1))(x/(330 ms^(-1))-t)]` The waves superimpose. (i) Find distance between two nearest points where an intensity maximum is recorded simultaneously. (ii) Find the time gap between two successive intensity maxima at a given point.

Answer» Correct Answer - (i) 150 m
(ii) 0.5 s
10.

Two trains A and B are moving on parallel tracks in opposite direction at same speed of `30 ms^( –1)`. Just when the engines of the two trains are about to cross, the engine of train A begins to sound a horn. The sound of the horn is composed of components varying in frequency from `900 Hz` to 1200 Hz. The speed of sound in air is `330 ms^( –1)`. (a) Find the frequency spread (range of frequencies) for the sound heard by a passenger in train A. (b) Find the frequency spread heard by a passenger in train B.

Answer» Correct Answer - (a) 900 Hz to 1200 Hz
(b) 1080 Hz to 1440 Hz
11.

Two tuning forks produce 4 beats per second when they are sounded together. Now both the forks are moved towards the observer at same speed (u). The beat frequency now becomes 5 Hz. If the observer also begins to run with speed u towards both the forks, what beat frequency will he hear now?

Answer» Correct Answer - 6 Hz
12.

A source of sound is approaching an observer with speed of 30 m/s and the observer is approaching the source with a speed 60 m/s. Then the fractional change in the frequency of sound in air (330 m/s) isA. `(1)/(3)`B. `(2)/(5)`C. `(2)/(2)`D. `(3)/(10)`

Answer» Correct Answer - D
13.

(i) A straight railway track is at a distance ‘d’ from you. A distant train approaches you travelling at a speed `u (lt` speed of sound`)` and crosses you. How does the apparent frequency `(f)` of the whistle change with time (`f_(0)` is the original frequency of the whistle). Draw a rough `f` vs `t` graph. (ii) A bat is tracking a bug. It emits a sound, which reflects off the bug. The bat hears the echo of the sound `0.1` seconds after it originally emitted it. The bat can tell if the insect is to the right or left by comparing when the sound reaches its right ear to when the sound reaches its left ear. Bat’s ears are only `2 cm` apart. Bats also use the frequency change of the sound echo to determine the flight direction of the bug. While hovering in the air (not moving), the bat emits a sound of `40.0 kHz`. The frequency of the echo is `40.4 kHz`. Assume that the speed of sound is `340 m//s`. (a) How far away is the bug? (b) How much time delay is there between the echo reaching the two ears if the bug is directly to the right of the bat? (c) What is the speed of the bug?

Answer» Correct Answer - (ii) (a) 17 m
(b) `5.9 xx10^(-5) s`
(c) `1.7 m//s`
14.

A source of sound is located in a medium in which speed of sound is V and an observer is located in a medium in which speed of sound is 2V. Both the source and observer are moving directly towards each other at velocity `V/5`. The source has a frequency of `f_(0)`. (a) Find the wavelength of wave in the medium in which the observer is located. (b) Find the frequency received by the observer.

Answer» Correct Answer - (a) `8/5 V/f_(0)`
(b) `11/8 f_(0)`
15.

How many time are taken intense is 90dB sound than 40dB sound?A. 5B. 50C. 500D. `10^(5)`

Answer» Correct Answer - D
16.

Assertion : A progressive wave can be represented by `y= log (x+vt) ` Reason: Any progressive wave must have the form `y= f(x-vt )or y= f (x+vt) ` where symbols have their usual meaningA. Assertion is True Reason is True, Reason is a correct explanation for AssertionB. Assertion is True Reason is True : Reason is not a correct explanation for AssertionC. Assertion is True ,Reason is FalseD. Assertion is False but , Reason is True

Answer» Correct Answer - D
17.

The length of a stretched wire is 1 m and its fundamental frequency is 300 Hz.What is the speed of the transverse wave in the wire ?

Answer» Correct Answer - `600 ms^(-1)`
18.

A wave of frequency 400 Hz has a phase velocity of 300 m/s The phase difference between two displacement at a certain point at time t= `10^(-3) `s isA. ` 72^(@) `B. ` 102^(@) `C. `144^(@)`D. ` 180^(@) `

Answer» Correct Answer - C
19.

Wave of frequency 500 Hz has a phase velocity `360 m//s`. The phase difference between two displacement at a certain point at time `10^(-3)s` apart will beA. `pi` radB. `(pi)/(2)` radC. `(pi)/(4)` radD. `2pi` rad

Answer» Correct Answer - A
`Delta x = ct " "….(i)`
`therefore" " Delta phi = (2pi)/(lambda) Delta x = (2pi)/(c//f)Deltax`
`= (2pict)/(c//f)=2pi ft` [from Eq. (i)]
`= 2pi xx 500 xx 10^(-3)`
`pi` rad
20.

A wave of angular frequency `omega` propagates so that a certain phase of oscillation moves along x-axis, y-axis, z-axis with speeds `c_(1) c_(2)` and `c_(3)` respectively.A. `(omega)/(sqrt(c_(1)^(2)+c_(2)^(2)+c_(3)^(2)))(hat(i)+hat(j)+hat(k))`B. `(omega)/(c_(1))hat(i)+(omega)/(c_(2))hat(j)+(omega)/(c_(3))hat(k)`C. `(omegahat(i) + omegahat(j) +omegahat(k))(1)/(c )`D. None of these

Answer» Correct Answer - B
Propagation constant is a vector quantity.
`therefore " "k=k_(x)hat(i)+k_(y)hat(j)+k_(2)hat(k)`
Here, `k_(x) = (omega)/(v_(x)) = (omega)/(c_(1))`
`k_(y) = (omega)/(v_(y)) = (omega)/(c_(2))`
and `k_(z) = (omega)/(v_(z))= (omega)/(c_(3))`
`therefore " "k = (omega)/(c_(1))hat(i) + (omega)/(c_(2))hat(j) + (omega)/(c_(3))hat(k)`
21.

The freuquency of tuning forks A and B are respectively `3%` more and `2%` less than the frequency of tuning fork `C`. When A and B are simultaneously excited, 5 beats per second are produced. Then the frequency of the tuning fork `A` (in Hz)` IsA. 98B. 100C. 103D. 105

Answer» Correct Answer - D
22.

The transvers displacement of a string (clamped at its both ends) is given by `y(x,t) = 0.06 sin ((2pi)/(3)s) cos (120 pit)` Where `x` and `y` are in `m` and `t` in `s`. The length of the string `1.5 m` and its mass is `3.0 xx 10^(-2) kg`. Answer the following : (a) Does the funcation represent a travelling wave or a stational wave ? (b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength. Frequency and speed of each wave ? Datermine the tension in the string.A. 2m, 120 HzB. `(2)/(3)m, 60 Hz `C. ` (3)/(2) m. 120 Hz `D. ` 3m , 60 Hz `

Answer» Correct Answer - D
23.

A long string having a cross- sectional area `0.80 mm^2` and density `12.5 g cm^(-3)` is subjected to a tension of 64 N along the X-axis. One end of this string is attached to a vibrator moving in transverse direction at a frequency fo 20Hz. At t = 0. the source is at a maximujm displacement y= 1.0 cm. (a) Write the equation for the wave. (c ) What is the displacement of the particle of the string at x = 50 cm at time t = 0.05 s ? (d) What is the velocity of this particle at this instant ?

Answer» Correct Answer - A::B::C::D
(a) `v-=sqrt((T)/(rhoS)`
`=sqrt((64)/(12.5xx10^(3)xx0.8xx10^(-6))`
`=80 m//s`
(b) `omega = 2pif = 2pi(20) = 40pi rad//s`
`k=(omega)/(v) = (40pi)/(80) =(pi)/(2)m^(-1) `
`:. y = (1.0 cm) cos[(40pis^(-1))t-((pi)/(2)m^(-1))x]`
(c) Substituting `x=0.5 m and t=0.05 s`, we get
`y=(1)/(sqrt2) cm`
(d) Particle velocity at time `t`,
`v_(P) = (dely)/(delt)`
`=-(40pi cm//s) sin [(40pis^(-1))t-((pi)/(2)m^(-1))x]`
Substituting `x=0.5 m` and `t= 0.05 s`, we get
`v_(P) =89cm//s`
24.

Two strings of same material are joined to form a large string and is stretched between rigid supports. The diameter of the second string is twice that of the first. It was observed in an experiment that the whole string was oscillating in 4 loops with a node at the joint. Find the possible lengths of the second string if the length of first string is 90 cm.

Answer» Correct Answer - `15 cm, 4 cm, 135 cm`
25.

Two long strings `A` and B`, each having linear mass density `1.2 xx 10^(-2)kg//m` are stretched by different tensions `4.8 N` and `7.5N` respectively and are kept parallel to each other with their left ends at `x = 0`. Wave pulse are produced on the string at the left ends at `t = 0` on string `A` and at `t=20ms` on string `B`. When and where will the pulse on `B` overtake that on `A`?

Answer» Correct Answer - A::B
`v_(1) =sqrt((T)/(mu_(1))`
`=sqrt((4.8)/(1.2 xx 10^(-2))) = 20 m//s`
`v_(2) = sqrt(T_(2)/(mu_(2))) = sqrt((7.5)/(1.2 xx 10^(-2))`
`=25m//s`
Pulse will meet when `x_(A) =x_(B)`
or `20t = 25(t -0.02)`
`:. t =0.1s`
and `x_(A)` or `x_(B) = 20 xx0.1 =2m`
26.

One end of each of two identical springs, each of force constant `0.5N//m` are attached on the opposite sides the a wooden block of mass `0.01kg`. The other ends of the spring are connected to separate rigid supports such that the springs are unstrtched and are collinear in a horizontal plane. To the wooden piece is fixed a pointer which touches a vertically moving plane paper. The wooden piece kept on a smooth horizontal table is now displaced by `0.02m` along the line of springs and released. If the speed of paper is `0.1m//s`, find the equation of the path traced by the pointer on the paper and the distance between two consecutive maximum on this path.

Answer» Correct Answer - A::B::C
`k_(eff) = 2k = 1.0 N//m`
`f = (1)/(2pi) sqrt(k_(eff)/(m)) = (10)/(2pi)s^(-1)`
`v=0.1 m/s , A =0.02 m`
`lambda=(v)/(f) = (0.1)/(((10)/(2pi))) = (2pi)/(100)m`
`y = A cos ((2pi)/(lambda)) (vt - x)`
`=0.02 cos 100(0.1t - x)`
`=0.02 cos (10t - 100x)m`
The distance between two successive maxima
`= lambda = (2pi)/(100) =0.0628 m`
27.

The position of a transverse wave travelling in medium along positive x-axis is shown in figure at time t=0. Speed of wave is v=200 m/s Frequency of the wave is A. `10^(2) Hz`B. `10^(3) Hz`C. `10^(4) Hz`D. `10^(5) Hz`

Answer» Correct Answer - B
28.

The position of a transverse wave travelling in medium along positive x-axis is shown in figure at time t=0. Speed of wave is v=200 m/s Equation of the wave is (in SI unit) A. `y=0.04 sin 2 pi (5xx-10^(3)t)`B. `y=0.04 sin 2 pi (10^(3) t-5xx)`C. `y=0.04 cos 2 pi (5xx-10^(3)t)`D. `y=0.04 cos 2 pi (10^(3) t-5xx)`

Answer» Correct Answer - A
29.

Figure shows a plot of the transverse displacement of the particle of a string at `t = 0` through which a travelling wave is passing in the positive in the positive x-direction. The wave speed is `20cm//s`. Find (a) the amplitude (b) the wavelength (c) the wave number and (d) the frequency of the wave.

Answer» Correct Answer - A::B::C::D
From the given figure, we can see that
(a) Amplitude, `A = 1.0 mm`
(b) Wavelength, `lambda = 4cm`
(c) Wave number, `k = (2pi)/(lambda) = 1.57 cm^(-1)~~ 1.6 cm^(-1)`
(d) Frequency, `f = (v)/(lambda) = (20)/(4) = 5Hz`
30.

Two wires of different densities but same area of cross-section are soldered together at one end and are stretched to a tension `T`. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the first wire to that of the second wire.

Answer» Correct Answer - B
`v = sqrt((T)/(rhoS))` or `v prop (1)/(sqrt(rho))`
`:. (v_(1))/(v_(2)) = sqrt((rho_(2))/(rho_(1)))`
`:. (rho_(1))/(rho_2) = ((v_(2))/(v_(1)))^(2) = ((1)/(2))^(3) = (1)/(4)`
31.

A string fixed at both ends vibrates in a resonant mode with a separation of 2.0cm between the consecutive nodes. For the next higher resonants frequecy this separation to 1.6cm. The length of the string isA. 4.0cmB. 8.0cmC. 12.0cmD. 16.0cm

Answer» Correct Answer - B
32.

A string of mass 0.2 kg/m and length l= 0.6 m is fixed at both ends and streteched such that it has a tension of 80 N. the string vibrates in 3 segments with maximum amplitude of 0.5 cm. the maximum transevers velcotiy amplitude isA. 1.57 m/sB. 6. 28 m/sC. 3.14 m/sD. 9.42 m/s

Answer» Correct Answer - A
33.

The two interfering waves have intensities in the ratio `9 : 4`. The ratio of intensities of maxima and minima in the interference pattern will beA. `1 : 25`B. `9 : 4`C. `25 : 1`D. `4 : 9`

Answer» Correct Answer - C
`(I_("max"))/(I_("min")) = ((sqrt((I_(1))/(I_(2)) + 1))/(sqrt((I_(1))/(I_(2)) -1)))^(2) = ((sqrt((9)/(4) + 1))/(sqrt((9)/(4) - 2)))^(2) = (25)/(1)`
34.

Under what condition, maximum particle velocity is four times the wave velocity corresponding to the equation, `y=A sin(omegat-kx)`

Answer» Maximum particle velocity is `omegaA` and wave velovity is `(omega)/(k)`.
Now, given that
maximum particle velocity`=4` (wave velocity)
or `omegaA=4((omega)/(k))`
`:. A=(4)/(k)`
So, this is the required condition.
35.

A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of `10cm//s`. The wavelength of the wave is 0.5 m and its amplitude is `10 cm`. At a particular time t,the snapshot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is (a) `sqrt(3pi)/(50)hatjm//s` (b)`-sqrt(3pi)/(50)hatjm//s` (c)`sqrt(3pi)/(50)hatim//s` (d) `-sqrt(3pi)/(50)hatim//s`

Answer» Particle velocity `v_p =-v` (slope of y-x graph)
Here, `v+=ve`,as the wave is travelling in positive x-direction. Slope at P is negative.
`:.` Velocity of particle is in positive `y`(or `hatj`) direction.
`:.` Correct option is (a).
36.

`S_(1)` and `S_(2)` are two sources of sound emitting sine waves. The two sources are in phase. The sound emitted by the two sources interfers at point `F`. The waves of wavelength : A. 1 m will result in constructive interferenceB. `2/3` m will result in constructive interferenceC. 2 m will result in destructive interferenceD. 4 m will result in destructive interference

Answer» Correct Answer - A::B::D
37.

In (Q. 24.) if at t = 0, y = 2.5 mm, the equation of standing wave isA. `(2.5 mm) sin. (2pi)/(l) x cos (2pisqrt(((T)/(mul^(2)))))t`B. `5 mm sin .(pi)/(l) x cos 2pit`C. `5 mm sin. (2pi)/(l) x cos (2pisqrt(((T)/(mul^(2)))))t`D. `5 mm cos. (2pi)/(l) x cos (2pisqrt(((T)/(mul^(2)))))t`

Answer» Correct Answer - C
The equation of standing wave on a string fixed both ends is
`y = 2a sin kx cos omegat`
Here, 2a = 5 mm
`k = (2pi)/(l)`
`omega=2piv=2pi sqrt(((T)/(mu l^(2))))`
`therefore " "y = (5 mm) sin. (2pi)/(l) x cos 2 pi sqrt(((T)/(mu l^(2)))t)`
38.

A pulse is incident on a rigid walt. The possible from of reflected pulse is A. B. C. D.

Answer» Correct Answer - C
39.

When a longitudinal wave is incident on a rigid wall.A. compression is reflected as rarefaction with phase change of `0^(@)`B. compression is reflected as rarefactin with phase change of `180^(@)`C. compression is reflected as compression with no phase changeD. compression is reflected as compression with phase change of `180^(@)`

Answer» Correct Answer - D
40.

When sound is reflected from a denser mediumA. crest is reflected as a troughB. crest is reflected as a crestC. compression is reflected as a rarefactionD. compression is reflected as a compression

Answer» Correct Answer - D
41.

When sound is reflected from a denser medium,A. crest is reflected as a thoughB. crest is reflected as crestC. compression is reflected as a rarefaction.D. compression is reflected as a compression

Answer» Correct Answer - C
42.

The sound waves reflected from denser medium. (A) Particle velocity changes (B) Wave velocity changes (C) Compression is reflected as rarefaction (D) Change of phase of `180^(@)` between incident and reflected waves Which of the above statements are correct ?A. all of the aboveB. A, B and DC. B and D onlyD. B, C and D

Answer» Correct Answer - B
43.

The sound waves reflected from denser medium. (A) Particle velocity changes (B) Wave velocity changes (C) Compression is reflected as rarefaction (D) Change of phase of `180^(@)` between incident and reflected waves Which of the above statements are correct ?A. all of the aboveB. A, B and DC. B and CD. B, C and D

Answer» Correct Answer - C
44.

When a longistudinal wave is incident at the bondary of a denser medium, thenA. compression reflects as a compressionB. compression reflects as a rarefactionC. rarefaction reflects as a compressionD. longitudinal wave reflects as transverse wave

Answer» Correct Answer - A
45.

Two aeroplanes A and B ,each moving with a speed of 720 km/hr. are moving directly away from each other.Aeroplane A emits a whistle of frequency 1080 Hz.The apparent frequency heard by a person in plane B will be (velocity of sound in air =340 m/s )A. 200 HzB. 260 HzC. 280 HzD. 300 Hz

Answer» Correct Answer - D
46.

Two aeroplanes are moving towards each other and cross each other. Then the apparent pitchA. first decreases and after crossing it increasesB. first increases and after crossing it decreasesC. first remains constant and then decreasesD. continuously increases

Answer» Correct Answer - B
47.

An observer is standing on a railway platform. He hears the whistle of railway engine moving towards him and then passing. He fells thatA. the pitch appears to increase and then decreaseB. the pitch appears to decrease continuouslyC. the pitch does not changeD. the pitch appears to increase continuously

Answer» Correct Answer - A
48.

A person is standing on a platform. As engine while approaching the platform blows a whistle , the frequency of which is 100 Hz.The speed of engine is `108 km h^(-1)` and speed of sound is `340 ms^(-1)`.Calculate the appearent frequency of the whistle as heard by the person.

Answer» Correct Answer - 109.7 Hz
49.

If the star approaches the earth. The Doppler lines are shiftedA. towards the red colour of spectrumB. towards the violet colour of spectrumC. infrared region of spectrumD. ultraviolet region of spectrum

Answer» Correct Answer - B
50.

Assertion: The whistly of an approaching engine appears to be shriller that that of a receding engine. Reason :This is due to Doppler effect,which states that if a source of sound approaches the observer the frequency of sound increase and if the source recedes the observer ,the frequency of sound decreases.A. Assertion is true,Reason is true, Reason is a correct explanation for AssertionB. Assertion is true,Reason is true, Reason is a not correct explanation for AssertionC. Assertion is True ,Reason is FalseD. Assertion is False but , Reason is True

Answer» Correct Answer - A