M.C.Q (1 Marks) - Page 2 - Physics STD 11 Science Questions - Vidyadip

Questions · Page 2 of 2

M.C.Q (1 Marks)

MCQ 511 Mark

If equation of sound wave is $\text{y}=0.0015\sin(62.4\text{x}+316\text{t}),$ then its wavelength will be:

A
$0.2$ unit
B
$0.3$ unit
✓
$0.1$ unit
D
$2$ unit

Answer

Correct option: C.

$0.1$ unit

The given equation is $\text{y}=0.0015\sin(62.4\text{x}+316\text{t}),$ Compare it with the standard equation.
$\text{y}=\text{r}\sin\Big(\frac{2\pi}{\lambda}\text{x}+\frac{2\pi\text{t}}{\text{T}}\Big)$
$\frac{2\pi}{\lambda}=62.4$
$\lambda=\frac{2\pi}{62.4}=\frac{2\times3.14}{62.4}=0.1$ unit

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MCQ 521 Mark

The whistle of a railway engine is heard in winter at much longer distances. This is due to:

✓
Decrease in velocity of sound in winter.
B
Decrease in the density of air w.r.t. height from the surface of the earth.
C
Cold air absorbs much smaller energy from sound waves.
D
Increase in the density of air w.r.t. height from the surface of the earth.

Answer

Correct option: A.

Decrease in velocity of sound in winter.

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MCQ 531 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.

The density of medium particles are maximum and minimum at compression and rarefaction point, so rejects option $(a).$
Also density changes very rapidly, so temperature of medium increases. So, rejects option $(b).$
Bulk modules of air remains constant, rejects option $(c).$
The time of compressions and rarefaction is very small so heat does not transfer.

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MCQ 541 Mark

Doppler's effect holds good for:

A
Only sound waves.
B
Only electromagnetic waves.
✓
Both sound waves and electromagnetic waves.
D
None of the above.

Answer

Correct option: C.

Both sound waves and electromagnetic waves.

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MCQ 551 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 $120\pi\text{t}$ ay atime, 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 561 Mark

A string is stretched between fixed points separated by $75.0\ cm.$ It is observed to have resonant frequencies of $420Hz$ and $315Hz.$ There are no other resonant frequencies between these two. Then the lowest resonance frequency for this string is:

A
$1.05Hz$
B
$1050Hz$
C
$10.5Hz$
✓
$105Hz$

Answer

Correct option: D.

$105Hz$

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MCQ 571 Mark

At nodes in stationary waves:

A
Change in pressure and density are maximum.
✓
Change in pressure and density are minimum.
C
Strain is zero.
D
Energy is maximum.

Answer

Correct option: B.

Change in pressure and density are minimum.

In stationary waves, all particles except nodes oscillate with same frequency but amplitude is zero at nodes and maximum at anti$-$nodes. Thus, change in pressure and density is minimum at nodes. Following two wave trains are approaching each other.

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MCQ 581 Mark

When two harmonic sound waves of close $($but not equal$)$ frequencies are heard at the same time, we hear:

A
A sound of similar frequency.
B
A sound of frequency which is the average of two close frequencies.
C
Audibly distinct waxing and waning of the intensity of the sound with a frequency equal to the difference in the two close frequencies.
✓
All of the above.

Answer

Correct option: D.

All of the above.

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MCQ 591 Mark

A particle has displacement y given by $\text{y}=3\sin(5\pi\text{t}+\phi),$ where $y$ is in metre and $t$ is in second. What are frequency and period of motion?

A
$0.4Hz, 2.5s$
✓
$2.5Hz, 0.4s$
C
$2.5Hz, 2.5s$
D
$0.4Hz, 0.4s$

Answer

Correct option: B.

$2.5Hz, 0.4s$

Comparison with the standard equation shows that
$\frac{2\pi}{\text{T}}=5\pi,\text{T}=\frac{2\pi}{5\pi}=0.4\text{s}$
$\text{n}=\frac{1}{\text{T}}=\frac{1}{4}=2.5\text{Hz}$

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MCQ 601 Mark

The equation of a progressive wave can be given by $\text{y}=15\sin(600\pi\text{t}-0.02\pi\text{x})\text{cm}.$ The frequency of the wave is:

✓
$330Hz$
B
$342Hz$
C
$365Hz$
D
$660Hz$

Answer

Correct option: A.

$330Hz$

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MCQ 611 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 $180^\circ$
$\text{y}_\text{i}=0.6\sin2\pi\Big[\text{t}+\frac{\text{x}}{2}\Big]$
$\text{y}_\text{r}\Big(\frac{2}{3}\times0.6\Big)\sin2\pi\Big[\pi+\text{t}+\frac{\text{x}}{2}\Big]$
$\text{y}_\text{r}=-0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big).$
Hence verifies the option $(b).$

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MCQ 621 Mark

An empty vessel is partially filled with water. The frequency of vibration of air column in the vessel:

✓
Decreases.
B
Increases.
C
Depends on the purity of water.
D
Remains the same.

Answer

Correct option: A.

Decreases.

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MCQ 631 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 $180\ m/ s$ 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 $\text{y}(\text{x, t})=0.06\sin\Big(\frac{2\pi}{3}\Big)\cos[9120\pi)\text{t})$

Comparring both equation $\omega=120\pi$

$2\pi\text{v}=120\pi$ or $\text{v}=\frac{120}{2}=60\text{Hz}$
Verifies the option $(b).$

$\frac{2\pi}{\lambda}=\text{k}$ 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 $(D).$

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MCQ 641 Mark

In case of a moving source of sound approaching the observer:

✓
Wavelength of sound appears to be less.
B
Wavelength of sound appears to be more.
C
The frequency appears to be less.
D
None of these.

Answer

Correct option: A.

Wavelength of sound appears to be less.

When source approaches the observer, apparent wavelength of sound decreases.

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MCQ 651 Mark

A sound source is moving towards a stationary listener with $\frac{1}{10}$ of the speed of sound. The ratio of apparent to real frequency is:

✓
$\frac{10}{9}$
B
$\Big(\frac{10}{9}\Big)^2$
C
$\Big(\frac{11}{10}\Big)^2$
D
$\frac{11}{10}$

Answer

Correct option: A.

$\frac{10}{9}$

When source is moving towards a stationary listener, apparent frequency.
$\text{f}'=\frac{\nu\times\text{f}}{\nu-\nu_\text{s}}=\frac{\nu}{\nu-\frac{\nu}{10}}\text{f}=\frac{10}{9}\text{f}$
$\frac{\text{f}'}{\text{f}}=\frac{10}{9}$

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MCQ 661 Mark

A tuning fork produces $4\text{beats/ sec}$ with another fork of frequency $288\ \text{c.p.s}$. A little wax is placed on the unknown fork and it then produces $2\text{beats/ sec.}$ The unknown frequency is:

A
$368\ \text{c.p.s.}$
✓
$292\ \text{c.p.s}$
C
$284\ \text{c.p.s.}$
D
$290\ \text{c.p.s.}$

Answer

Correct option: B.

$292\ \text{c.p.s}$

Known frequency of $A, n_1 = 288\ \text{c.p.s.}$
Number of beats/ sec $m = 4$
$\therefore$ Unknown freq. of $B, n_2 = 288\pm4=292$ or $284$
on loading $B$, number of $\text{beats/ sec}$ decreases to $2.$
Therefore, $m$ is $+.$
$\therefore n_2 = 288 + 4 = 292\ \text{c.p.s.}$

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MCQ 671 Mark

The displacement $y$ of a wave travelling in $x-$direction is given by $\text{y}=10^{-4}\sin\Big(600\text{t}-2\text{x}+\frac{\pi}{3}\Big)$ where $x$ and $y$ are in metre and $t$ is in seconds. The speed of wave motion in $s^{-1}$ is:

✓
$300$
B
$600$
C
$1200$
D
$200$

Answer

Correct option: A.

$300$

Here, $\text{y}=10^{-4}\sin\Big(600\text{t}-2\text{x}+\frac{\pi}{3}\Big)$
Compare it with the standard equation of a travalling wave
$\text{y}=\text{r}\Big(\frac{2\pi\text{t}}{\text{T}}-\frac{2\pi\text{x}}{\lambda}\neq\phi\Big)$
$\frac{2\pi}{\text{T}}=600,\text{T}=\frac{2\pi}{600}=\frac{\pi}{300}\text{s}$
$\frac{2\pi}{\lambda}=+2\lambda =\frac{2\pi}{2}=\pi\text{m}$
$\nu=\frac{\lambda}{\text{T}}=\frac{\pi}{\frac{\pi}{300}}=300\text{m/s}$

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MCQ 681 Mark

The air column in a pipe open at both ends is oscillating with certain frequency. Which of the given statement $(s)$ is/ are correct for the open air column at both ends?

A
Each end of the pipe acts is an a node.
B
An open air column at both ends generates all harmonics.
C
Each end of the pipe is a node nine is a node.
✓
Both $(a)$ and $(b).$

Answer

Correct option: D.

Both $(a)$ and $(b).$

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MCQ 691 Mark

A wire under tension $T$ emits a note of fundamental frequency $200Hz.$ If the tension is increased by $3T,$ the fundamental frequency will be:

✓
$400\text{Hz}$
B
$0\text{Hz}$
C
$100\sqrt{3}\text{Hz}$
D
$200\sqrt{3}\text{Hz}$

Answer

Correct option: A.

$400\text{Hz}$

Here, $\text{v}=\frac{1}{2\text{l}}\sqrt{\frac{\text{T}}{\text{m}}}$
When tension is increased by $3T$
$\text{v}'=\frac{1}{2\text{l}}\sqrt{\frac{(\text{T}+3\text{T})}{\text{m}}}=2\text{v}$
$\text{v}'=2\times200=400\text{Hz}$

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MCQ 701 Mark

Equation of progressive wave is $\text{y}=\text{a}\sin\Big(10\pi\text{x}+11\pi\text{t}+\frac{\pi}{3}\Big)$ The wavelength of the wave is:

✓
$0.2$ unit
B
$0.1$ unit
C
$0.5$ unit
D
$1$ unit

Answer

Correct option: A.

$0.2$ unit

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MCQ 711 Mark

The frequency of a sound wave is $n$ and its velocity is $v.$ If the frequency is increased to $4n,$ the velocity of the wave will be:

✓
$\nu$
B
$2\nu$
C
$4\nu$
D
$\frac{\nu}{4}$

Answer

Correct option: A.

$\nu$

Velocity of sound is independent of frequency.
Therefore, it is same $(\nu)$ for frequency $n$ and $4n.$

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M.C.Q (1 Marks) - Page 2 - Physics STD 11 Science Questions - Vidyadip