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Physics M.C.Q (1 Marks)

Waves · UP Board (UPMSP) STD 11 Science (UPMSP - English Medium). 16 questions.

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M.C.Q (1 Marks)

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16 questions · auto-graded multiple-choice test.

MCQ 11 Mark
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 Identify the expected curve:
 
  • A
  • B
  • ✓
  • D
Answer
Correct option: C.
When qbserver is at rest and source of sound id moving towards observer then observed frequency n'.
$\text{n}'=\Big(\frac{\text{v}}{\text{V}-\text{v}_\text{s}}\Big)\text{n}_0$
Where $n_0$ original frequency of source of sound
v = speed of sound in medium
$\therefore​​​​​​\text{n}'>\text{n}_0\ \ \text{v}_\text{s}=$ speed of source
When source is moving away from observer
$\text{n}'=\frac{\text{v}}{(\text{v}+\text{v}_\text{s})}\text{n}_0\ \text{n}''<\text{n}_0$
Hence, the frequencies in both cases are same and $\text{n}'>\text{n}''.$ so graph (c) verifies the answer.
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MCQ 21 Mark
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 $\text{S.H.M.}$
  • ✓
    All of the above
Answer
Correct option: D.
All of the above
During propagation of mechanical wave each particles displaces from zero to maximum i.e., upto amplitude So amplitude of each particle is equal. Verifies the option $(b).$

For progressive wave medium particles oscillates about their mean position in which restoring force $\text{F}\propto(-\text{y}).$
So motion of medium particles is simple harmonic motion.
So verifies the option$(c)$.For progressive wave propagating in a medium of density $(\rho)$ and Bulk modulus $k$ the velocity $(\nu)$
As the depends on $k$ and $(\rho)$ and $k, (\rho)$ are different for different medium so of wave depends on nature of medium, hence, verifies the option $(d).$
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MCQ 31 Mark
Which of the following statements are true for a stationary wave?
  • A
    Every particle has a fixed amplitude which is different from the 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.
  • ✓
    All of the above
Answer
Correct option: D.
All of the above
In stationary waves $[\text{y}(\text{x, t})=\text{a}\sin\text{kx}\cos\omega\text{t}]$ the particles between two nodes vibrates with different amplitude which increases fron nodes.
The amplitude of a particle will remain constant a $\cos kx,$ but varies with $\lambda$
$\because\text{k}=\frac{2\pi}{\lambda}.$
Hence verifies the option $(a)$
particles between two nodes are in same phase.
i.e., motion of particles between two nodes will be either upward or downward and crosses the mean position at same time.
Hence the verifies option $(b)$
As the particles at nodes are rest so energy does not transfer verifies option $(c)$
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MCQ 41 Mark
Speed of sound waves in a fluid depends upon:
  • A
    Directty on density of the medium.
  • B
    Directly on the square root of bulk modulus of the medium.
  • C
    Inversly on the square root of density.
  • ✓
    Both $B$ and $C$
Answer
Correct option: D.
Both $B$ and $C$
Speed od sound wave in fluid of bulk modules $k$ and density $\rho$ is given by $\text{v}=\sqrt{\frac{\text{k}}{\rho}}$
so $\text{v}=\sqrt{\text{k}} ($if $\rho$ is constant$)$
And $\text{v}=\sqrt{\frac{1}{\rho}} ($if $k$ is constann$)$
so verifies the option $(b)$ and $(c).$
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MCQ 51 Mark
Water waves produced by a motor boat sailing in water are:
  • A
    Neither longitudinal nor transverse.
  • ✓
    Both longitudinal and transverse.
  • C
    Only longitudinal.
  • D
    Only transverse.
Answer
Correct option: B.
Both longitudinal and transverse.
As the waves are produced by motor boat on surface as well as inside water, the waves are both, transverse as well as longitudinal.
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MCQ 61 Mark
A string of mass 2.5kg is under a tension of 200N. The length of the stretched string is 20.0m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in:
  • A
    One second
  • ✓
    0.5 second
  • C
    2 seconds
  • D
    Data given is insufficient.
Answer
Correct option: B.
0.5 second
M = mass string 2.5kg, l = 20m
M = mas per unit length $=\frac{\text{M}}{\text{l}}=\frac{2.5}{20}=0.125\text{kg/ m}$
$\text{v}=\sqrt{\frac{\text{T}}{\mu}}=\sqrt{\frac{200}{0.125}}=\sqrt{1600}=40\text{m/ s}$
time $= \frac{\text{distance}}{\text{speed}}=\frac{20\text{m}}{40\text{m/ s}}=\frac{1}{2}\sec=0.5\sec.$
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MCQ 71 Mark
A transverse harmonic wave on a string is described by $\text{y}(\text{x},\text{t})=3.0\sin(36\ \text{t}+0.018\text{x}+\pi/ 4)$ 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 $20m/ s.$
  • C
    Frequency of the wave is $5.7Hz.$
  • ✓
    All of the above
Answer
Correct option: D.
All of the above
The standard from of a wave propagated from left to right i. e., in $+ ve$ direction
$\text{y}=\text{a}\sin(\omega\text{t}-\text{k}\text{x}+\phi)$ and
$\text{y}=3.0\sin\Big(36\text{t}+0.018\text{x}+\frac{\pi}{4}\Big) ($given$)$
  1. As in given equation $x$ is in positive sigh so given wave travalling from right to left verifies option $(a)$
  2. $\text{k}=0.018=\frac{2\pi}{\lambda}=0.018\Rightarrow\lambda=\frac{2\pi}{0.018}$
$\therefore\text{v}=\text{v}\lambda=\frac{18}{\pi}\times\frac{2\pi}{0.018}=2000\text{cm}/ \ \text{s}=20\text{m/ s}$
Verifies the option $(b)$
  1. $\omega=36$ or $2\pi\text{n}=36$ or $\text{v}=\frac{36}{2\pi}=\frac{18}{3.14}=5.7\text{Hz}$
Verifies option $(c)\ n = 5.7Hz$
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MCQ 81 Mark
With propagation of longitudinal waves through a medium, the quantity transmitted is:
  • A
    Matter.
  • ✓
    Energy.
  • C
    Energy and matter.
  • D
    Energy, matter and momentum.
Answer
Correct option: B.
Energy.
During propagation of any wave in a medium only energy is transmitted from one point to another. Matter does not change its own position it, vibrates about its mean position only.
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MCQ 91 Mark
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.
  • ✓
    Mechanical transverse waves can propagate through solids only.
  • D
    Longitudinal waves can propagate through vacuum.
Answer
Correct option: C.
Mechanical transverse waves can propagate through solids only.
In case of mechanical transverse wave propagates through a medium, the medium particles oscillate right angles to the direction of wave motion or energy propagation. It travels in the form of crests and troughs.
When mechanical transverse wave propagates through a medium element of the medium is subjected to shearing stress. Solids and strings have shear modulus, that is why, sustain shearing stress. Fluids have no shape of their own, they yield to shearing stress. Transverse waves can be transmitted through solids, they can be setup on the surface of liquids. But they cannot be transmitted into liquids and gases.
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MCQ 101 Mark
Sound waves of wavelength $\pi$ travelling in a medium with a speed of v m/ s enter into another medium where its speed is 2v m/ s. Wavelength of sound waves in the second medium is:
  • A
    $\pi$
  • B
    $\frac{\pi}{2}$
  • ✓
    $2\pi$
  • D
    $4\pi$
Answer
Correct option: C.
$2\pi$
When wave passes from one medium to another its frequency (v) does not chang but its velocity and wavelength changs.
$\text{v}=\text{v}\lambda$ or $\text{v}=\frac{\text{v}}{\lambda}$
$\frac{\text{v}}{\lambda}=\frac{2\text{v}}{\lambda_2}\Rightarrow\lambda_2=2\lambda.$
Hence verifies the correct option (c)
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MCQ 111 Mark
A train, standing in a station yard, blows a whistle of frequency $400Hz$ in still air. The wind starts blowing in the direction from the yard to the station with a speed of $10m/ s.$ Given that the speed of sound in still air is $340m/ s,$
  • A
    The frequency of sound as heard by an observer standing on the platform is $400Hz.$
  • B
    The speed of sound for the observer standing on the platform is $350m/ s.$
  • ✓
    Both $A$ and $B$
  • D
    The frequency of sound as heard by the observer standing on the platform will decrease.
Answer
Correct option: C.
Both $A$ and $B$
As the disatance between listener and source does not change so frequency of sound does not change the as heard listener. i.e.,he heard $\text{v}_0=400\text{Hz}.$ verifies option$(a)$
$\text{v}_0=400\text{Hz}$ frequency of source of sound.
Velocity of wind $\text{v}_\text{w}=10\text{m/ s}$ from source of listenr.
Speed of sound in still air $= \text{v}_\text{s}=340\text{m/ s}$
As the listenner is standing on platfrom.
Speed $od$ sound with respect to listener $\text{v}_\text{s}+\text{v}_\text{w}=340+10=350\text{m/ s}$
Verifies the option $(b)$
Reject the option $(c)$ as it constant $\text{v}_0=400\text{Hz}$
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MCQ 121 Mark
Speed of sound wave in air:
  • A
    Is independent of temperature.
  • B
    Increases with pressure.
  • ✓
    Increases with increase in humidity.
  • D
    Decreases with increase in humidity.
Answer
Correct option: C.
Increases with increase in humidity.
Speed of sound (longitudinal) wave in air is $\text{v}=\sqrt{\frac{\lambda\text{p}}{\text{p}}}.$ the density of water vapours is less (rises up) than the air so on increasing humidity, the density of medium decrease in turn increases the speed of sound in air by $\text{v}=\propto\frac{1}{\sqrt{\text{p}}}$ (relation).
Hence verifies the option (c).
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MCQ 131 Mark
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.
  • ✓
    There is no transfer of heat.
Answer
Correct option: D.
There is no transfer of heat.
 
  1. The density of medium particles are maximum and minimum at compression and rarefaction point, so rejects option $(a).$
  2. Also density changes very rapidly, so temperature of medium increases. So, rejects option $(b).$
  3. Bulk modules of air remains constant, rejects option $(c).$
  4. The time of compressions and rarefaction is very small so heat does not transfer.
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MCQ 141 Mark
The transverse displacement of a string $($clamped at its both ends$)$ is given by $\text{y}(\text{x, t})=0.06\sin(1\pi\text{x/ 3})\cos(120\pi\text{t}).$
All the points on the string between two consecutive nodes vibrate with
  • A
    Same frequency.
  • B
    Same phase.
  • C
    Different amplitude.
  • ✓
    All of the above
Answer
Correct option: D.
All of the above
The frequencies of all particles are same, verifies the option $(a).$
particles between any two consecutive nodes vibrates either upside or downside having sameb phase $120\pi\text{t}$ any time, verifies the option $(b)$
particles have ditternt energies. so rejects the option $(c)$
As the amplitude of different particles are diffrent between two nodes energy $(E) \propto\text{A}^2.$ 
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MCQ 151 Mark
Equation of a plane progressive wave is given by $\text{y}=0.6\sin2\pi\Big(\text{t}-\frac{\text{x}}{2}\Big).$ 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
    $\text{y}=0.6\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$
  • ✓
    $\text{y}=-0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$
  • C
    $\text{y}=0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$
  • D
    $\text{y}=-0.4\sin2\pi\Big(\text{t}-\frac{\text{x}}{2}\Big)$
Answer
Correct option: B.
$\text{y}=-0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$
After reflection of wave changes by phase 180°
$\text{y}_\text{i}=0.6\sin2\pi\Big[\text{t}+\frac{\text{x}}{2}\Big]$
$\text{y}_\text{r}\Big(\frac{2}{3}\times0.6\Big)\sin2\pi\Big[\pi+\text{t}+\frac{\text{x}}{2}\Big]$
$\text{y}_\text{r}=-0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big).$ Hence verifies the option (b).
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MCQ 161 Mark
The displacement of a string is given by $\text{y}(\text{x, t})=0.06\sin(2\pi\text{x}/ 3)\cos(120\pi\text{t})$ where $x$ and $y$ are in $m$ and $t$ in $s$. The length of the string is $1.5m$ and its mass is $3.0\times10^{-2}\text{kg}$
  • A
    It represents a progressive wave of frequency $60Hz.$
  • B
    It represents a stationary wave of frequency $60Hz.$
  • C
    It is the result of superposition of two waves of wavelength $3m,$ frequency $60Hz$ each travelling with a speed of $180m/ s$ in opposite direction.
  • ✓
    Both $B$ and $C$
Answer
Correct option: D.
Both $B$ and $C$
We know thet standard equation of stationary wave is $\text{y}(\text{x, t})=\text{a}\sin(\text{kx})\cos(\omega\text{t})$ and given equation is $\text{y}(\text{x, t})=0.06\sin\Big(\frac{2\pi}{3}\Big)\cos[9120\pi)\text{t})$
  1. Comparring both equation $\omega=120\pi$
$2\pi\text{v}=120\pi$ or $\text{v}=\frac{120}{2}=60\text{Hz}$
Verifies the option $(b).$
  1. $\frac{2\pi}{\lambda}=\text{k}$ from $\text{k}=\frac{2\pi}{3}$
$\therefore\frac{2\pi}{\lambda}=\frac{2\pi}{3}$
$\Rightarrow\lambda=3\text{m},\ \text{v}=60\text{Hz}$
speed $\text{v}=\text{v}\lambda=60\times3=180\text{m/ s}.$
​​​​​​​Hence, verifies the option $(c).$
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