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MCQ

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50 questions · auto-graded multiple-choice test.

MCQ 11 Mark
A string vibrates according to the equation $y=5 \sin \left(\frac{2 \pi x}{3}\right) \cos 20\  \pi t$, where $x$ and $y$ are in $\mathrm{cm}$ and $t$ in sec. The distance between two adjacent nodes is
  • A
    $3 \mathrm{~cm}$
  • B
    $4.5 \mathrm{~cm}$
  • C
    $6 \mathrm{~cm}$
  • $1.5 \mathrm{~cm}$
Answer
Correct option: D.
$1.5 \mathrm{~cm}$
(d) $y=5 \sin \left(\frac{2 \pi x}{3}\right) \cos 20 \pi t$, comparing with equation
$y=2 a \sin \frac{2 \pi x}{\lambda} \cos \frac{2 \pi v t}{\lambda} \Rightarrow \lambda=3$,
distance between two adjacent nodes $=\lambda / 2=1.5 \mathrm{~cm}$.
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MCQ 21 Mark
The equation of a travelling wave is given by $y=0.5 \sin (20 x-400 t)$ where $x$ and $y$ are in meter and $t$ is in second. The velocity of the wave is
  • A
    $10 \mathrm{~m} / \mathrm{s}$
  • $20 \mathrm{~m} / \mathrm{s}$
  • C
    $200 \mathrm{~m} / \mathrm{s}$
  • D
    $400 \mathrm{~m} / \mathrm{s}$
Answer
Correct option: B.
$20 \mathrm{~m} / \mathrm{s}$
(b) Given, $y=0.5 \sin (20 x-400 t)$
Comparing with $y=a \sin (\omega t-k x)$
Givesvelocity of wave $v=\frac{\omega}{k}=\frac{400}{20}=20 \mathrm{~m} / \mathrm{s}$.
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MCQ 31 Mark
A police car horn emits a sound at a frequency $240 \mathrm{~Hz}$ when the car is at rest. If the speed of the sound is $330 \mathrm{~m} / \mathrm{s}_{\llcorner}$the frequency heard by an observer who is approaching the car at a speed of $11 \mathrm{~m} / \mathrm{s}$, is :
  • $248 \mathrm{~Hz}$
  • B
    $244 \mathrm{~Hz}$
  • C
    $240 \mathrm{~Hz}$
  • D
    $230 \mathrm{~Hz}$
Answer
Correct option: A.
$248 \mathrm{~Hz}$
(a) Frequency heard by the observer
$[n^{\prime}=n\left(\frac{v+v_0}{v}\right)=240\left(\frac{330+11}{330}\right)=248 \mathrm{~Hz} .$
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MCQ 41 Mark
Two waves represented by the following equations are travelling in the same medium $y_1=5 \sin 2 \pi(75 t-0.25 x)$, $y_2=10 \sin 2 \pi(150 t-0.50 x)$ The intensity ratio $I_1 / I_2$ of the two waves is
  • A
    $1: 2$
  • $1: 4$
  • C
    $1: 8$
  • D
    $1: 16$
Answer
Correct option: B.
$1: 4$
(b) $\frac{I_1}{I_2}=\frac{a_1^2}{a_2^2} \Rightarrow \frac{I_1}{I_2}=\frac{25}{100}=\frac{1}{4}$
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MCQ 51 Mark
A source of sound of frequency $256 \mathrm{~Hz}$ is moving rapidly towards a wall with a velocity of $5 \mathrm{~m} / \mathrm{s}$. The speed of sound is $330 \mathrm{~m} / \mathrm{s}$. If the observer is between the wall and the source, then beats per second heard will be
  • $7.8 \mathrm{~Hz}$
  • B
    $7.7 \mathrm{~Hz}$
  • C
    $3.9 \mathrm{~Hz}$
  • D
    Zero
Answer
Correct option: A.
$7.8 \mathrm{~Hz}$
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MCQ 61 Mark
A small source of sound moves on a circle as shown in the figure and an observer is standing on $O$. Let $n_1, n_2$ and $n_3$ be the frequencies heard when the source is at $A, B$ and $C$ respectively. ThenImage
  • A
    $n_1>n_2>n_3$
  • $n_2>n_3>n_1$
  • C
    $n_1=n_2>n_3$
  • D
    $n_2>n_1>n_3$
Answer
Correct option: B.
$n_2>n_3>n_1$
At point $A$, source is moving away from observer so apparent frequency $n_1n$ and point $C$ source is moving perpendicular to observer so $n_3=n$ Hence $n_2>n_3>n_1$
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MCQ 71 Mark
Two trains are moving towards each other at speeds of $20 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$ relative to the ground. The first train sounds a whistle of frequency $600 \mathrm{~Hz}$. the frequency of the whistle heard by a passenger in the second train before the train meets is (the speed of sound in air is $340 \mathrm{~m} / \mathrm{s}$ )
  • A
    $600 \mathrm{~Hz}$
  • B
    $585 \mathrm{~Hz}$
  • C
    $645 \mathrm{~Hz}$
  • $666 \mathrm{~Hz}$
Answer
Correct option: D.
$666 \mathrm{~Hz}$
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MCQ 81 Mark
An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by $100 \mathrm{~Hz}$, then the fundamental frequency of open pipe is:
  • A
    $480 \mathrm{~Hz}$
  • B
    $300 \mathrm{~Hz}$
  • C
    $240 \mathrm{~Hz}$
  • $200 \mathrm{~Hz}$
Answer
Correct option: D.
$200 \mathrm{~Hz}$
(d) Fundamental frequency of open organ pipe $=\frac{v}{2 l}$
Frequency of third harmonic of closed pipe
$=\frac{3 v}{4 l}$$\therefore \frac{3 v}{4 l}=100+\frac{v}{2 l}$
$ \Rightarrow \frac{3 v}{4 l}-\frac{2 v}{4 l}=\frac{v}{4 l}=100$
$ \Rightarrow \frac{v}{2 l}=200 \mathrm{~Hz} \text {. }$
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MCQ 91 Mark
A wave equation which gives the displacement along $y-$ direction is given by $y=0.001 \sin (100 t+x)$ where $x$ and $y$ are in meterand $t$ is time in second. This represented a wave
  • A
    Of frequency $\frac{100}{\pi} \mathrm{Hz}$
  • B
    Of wavelength one metre
  • C
    Travelling with a velocity of $\frac{50}{\pi} m /s$ in the positive $X-$ direction
  • Travelling with a velocity of $100 \mathrm{~m/s}$ in the negative $X-$ direction
Answer
Correct option: D.
Travelling with a velocity of $100 \mathrm{~m/s}$ in the negative $X-$ direction
Travelling with a velocity of $100 \mathrm{~m/s}$ in the negative $X-$ direction
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MCQ 101 Mark
What is the base frequency if a pipe gives notes of frequencies $425, 255$ and $595$ and decide whether it is closed at one end or open at both ends
  • A
    $17$ , closed
  • $85$ , closed
  • C
    $17$, open
  • D
    $85$ , open
Answer
Correct option: B.
$85$ , closed
(b) Let the base frequency be $n$ for closed pipe then notes are $n, 3 n, 5 n \ldots .$.
$\therefore$ note $3 n=255 \Rightarrow n=85$, note $5 n=85 \times 5=425$
$note \ 7 n=7 \times 85=595$
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MCQ 111 Mark
An air column in a pipe, which is closed at one end, will be in resonance with a vibrating body of frequency $166 \mathrm{~Hz}$, if the length of the air column is
  • A
    $2.00 \mathrm{~m}$
  • B
    $1.50 \mathrm{~m}$
  • C
    $1.00 \mathrm{~m}$
  • $0.50 \mathrm{~m}$
Answer
Correct option: D.
$0.50 \mathrm{~m}$
(d) For closed pipe $n_1=\frac{v}{4 l} \Rightarrow l=\frac{v}{4 n}=\frac{332}{4 \times 166}=0.5 \mathrm{~m}$
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MCQ 121 Mark
It is possible to hear beats from the two vibrating sources of frequency
  • A
    $100 \mathrm{~Hz}$ and $150 \mathrm{~Hz}$
  • $20 \mathrm{~Hz}$ and $25 \mathrm{~Hz}$
  • C
    $400 \mathrm{~Hz}$ and $500 \mathrm{~Hz}$
  • D
    $1000 \mathrm{~Hz}$ and $1500 \mathrm{~Hz}$
Answer
Correct option: B.
$20 \mathrm{~Hz}$ and $25 \mathrm{~Hz}$
(b) For hearing beats, difference of frequencies should be approximately $10 \mathrm{~Hz}$.
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MCQ 131 Mark
A stretched string of length $l$, fixed at both ends can sustain stationary waves of wavelength $\lambda$, given by
  • A
    $\lambda=\frac{n^2}{2 l}$
  • B
    $\lambda=\frac{l^2}{2 n}$
  • $\lambda=\frac{2 l}{n}$
  • D
    $\lambda=2 l n$
Answer
Correct option: C.
$\lambda=\frac{2 l}{n}$
(c) $\lambda=\frac{2 l}{n} \quad(n=$ Number of loops $)$
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MCQ 141 Mark
A tuning fork vibrating with a sonometer having $20 \mathrm{~cm}$ wire produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to $21 \mathrm{~cm}$. the frequency of the tuning fork (in Hertz) must be
  • A
    $200$
  • B
    $210$
  • $205$
  • D
    $215$
Answer
Correct option: C.
$205$
Let the frequency of tunning fork be $N$As the frequency of vibration string $\propto \frac{1}{\text { lengthofstring }}$
For sonometer wire of length $20 \mathrm{~cm}$,frequency must be $(N+ 5)$ and that for the sonometer wire of length $21 \mathrm{~cm}$,the frequency must be $(N-5)$ as in each case the tunning fork produces $5$ beats/sec with so no meterwire
Hence $n_1 l_1=n_2 l_2 \Rightarrow(N+5) \times 20=(N-5) \times 21$
$\Rightarrow N=205\mathrm{~Hz} \text {. }$
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MCQ 151 Mark
A wire of density $9 \times 10 \mathrm{~kg} / \mathrm{m}$ is stretched between two clamps $1 \mathrm{~m}$ apart and is subjected to an extension of $4.9 \times 10 \mathrm{~m}$. The lowest frequency of transverse vibration in the wire is $\left(Y=9 \times 10^{-\mathrm{N}} / \mathrm{m}\right)$
  • A
    $40 \mathrm{~Hz}$
  • $35 \mathrm{~Hz}$
  • C
    $30 \mathrm{~Hz}$
  • D
    $25 \mathrm{~Hz}$
Answer
Correct option: B.
$35 \mathrm{~Hz}$
(b) For wire if $M=$ mass, $\rho=$ density, $A=$ Area of cross section$V=$ volume, $l=$ length, $\Delta I=$ change in lengthThen mass per unit length
$m=\frac{M}{l}=\frac{A l \rho}{l}=A \rho$
And Young's modules of elasticity
$y=\frac{T / A}{\Delta l / l}$$\Rightarrow T=\frac{Y \Delta l A}{l}$.
Hence lowest frequency of vibration
$n=\frac{1}{2 l} \sqrt{\frac{T}{m}}=\frac{1}{2 l} \sqrt{\frac{y\left(\frac{\Delta l}{l}\right) A}{A \rho}}=\frac{1}{2 l} \sqrt{\frac{y \Delta l}{l \rho}} $
$\Rightarrow n=\frac{1}{2 \times 1} \sqrt{\frac{9 \times 10^{10} \times 4.9 \times 10^{-4}}{1 \times 9 \times 10^3}}=35 \mathrm{~Hz}$
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MCQ 161 Mark
The harmonics which are present in a pipe open at one end are
  • Odd harmonics
  • B
    Even harmonics
  • C
    Even as well as odd harmonics
  • D
    None of these
Answer
Correct option: A.
Odd harmonics
(a) In closed pipe only odd harmonics are present
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MCQ 171 Mark
Two strings $X$ and $Y$ of a sitar produce a beat frequency $4 \mathrm{~Hz}$. When the tension of the string $Y$ is slightly increased the beat frequency is found to be $2 \mathrm{~Hz}$. If the frequency of $X$ is $300 \mathrm{~Hz}$, then the original frequency of $\gamma$ was
  • $296 \mathrm{~Hz}$
  • B
    $298 \mathrm{~Hz}$
  • C
    $302 \mathrm{~Hz}$
  • D
    $304 \mathrm{~Hz}$
Answer
Correct option: A.
$296 \mathrm{~Hz}$
(a) $n_x=300 \mathrm{~Hz}, n_y=$ ?$x$ = beat frequency $=4 \mathrm{~Hz}$, which is decreasing $(4 \rightarrow 2)$after increasing the tension of the string $y$.Also tension of wire $y$ increasing so $n_y \uparrow(\because n \propto \sqrt{T})$Hence $n_x-n_y \uparrow=x \downarrow \longrightarrow$ Correct
$ n_y \uparrow n_x=x\downarrow \longrightarrow \text { Wrong }$
$\Rightarrow n_y=n_x-x=300-4=296 \mathrm{~Hz}$
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MCQ 181 Mark
A wavelength $0.60 \mathrm{~cm}$ is produced in air and it travels at a speed of $300 \mathrm{~ms}$. It will be an
  • A
    Audible wave
  • B
    Infrasonic wave
  • Ultrasonic wave
  • D
    None of the above
Answer
Correct option: C.
Ultrasonic wave
(c)$n=\frac{v}{\lambda}=\frac{300}{0.6 \times 10^{-2}} \mathrm{~Hz}=\frac{3}{6} \times 10^4 \mathrm{~Hz}=50,000 \mathrm{~Hz}$$\Rightarrow$ Wave is ultrasonic.
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MCQ 191 Mark
The wavelengths of two waves are $50$ and $51 \mathrm{~cm}$ respectively. If the temperature of the room is $20 ^{\circ} \mathrm{C}$, then what will be the number of beats produced per second by these waves, when the speed of sound at $0^{\circ} \mathrm{C}$ is $332\  \mathrm{~m} / \mathrm{sec}$
  • $14$
  • B
    $10$
  • C
    $24$
  • D
    None of these
Answer
Correct option: A.
$14$
(a)$v_0=332 \mathrm{~m} / \mathrm{s} \text {. Velocity sound at } t^{\circ} \mathrm{C} \text { is } v_t=\left(v_0+0.61 \mathrm{t}\right) $
$\Rightarrow v_{20}=v_0+0.61 \times 20=344.2 \mathrm{~m} / \mathrm{s} $
$\Rightarrow \Delta n=v_{20}\left(\frac{1}{\lambda_1}-\frac{1}{\lambda_2}\right)=344.2\left(\frac{100}{50}-\frac{100}{51}\right)=14$
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MCQ 201 Mark
At which temperature the speed of sound in hydrogen will be same as that of speed of sound in oxygen at $100\ ^{\circ}\mathrm{C}$
  • A
    $-148\ ^{\circ}\mathrm{C}$
  • B
    $-212\ ^{\circ}\mathrm{C}$
  • C
    $-317.5\ ^{\circ}\mathrm{C}$
  • $-249.7\ ^{\circ}\mathrm{C}$
Answer
Correct option: D.
$-249.7\ ^{\circ}\mathrm{C}$
(d)$\text { Speed of sound in gases is } v=\sqrt{\frac{\gamma R T}{M}} \Rightarrow T \propto M $
$\text { (Because } v, \gamma \text {-constant}).$
 Hence $\frac{T_{H_2}}{T_{O_2}}=\frac{M_{\mathrm{H}_2}}{M_{\mathrm{O}_2}}$
$\Rightarrow\frac{T_{\mathrm{H}_2}}{(273+100)}=\frac{2}{32} $
$\Rightarrow T_{\mathrm{H}_2}=23.2 \mathrm{~K}=-249.7\ ^{\circ} \mathrm{C}$
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MCQ 211 Mark
When a longitudinal wave propagates through a medium, the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterised by an invariant
  • A
    Kinetic energy
  • Potential energy
  • C
    Sum of kinetic energy and potential energy
  • D
    Difference between kinetic energy and potential energy
Answer
Correct option: B.
Potential energy
Potential energy
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MCQ 221 Mark
The equation of a transverse wave is given by $ y=100 \sin \pi(0.04 z-2 t) $ where $y$ and $z$ are in $\mathrm{cm}$ ant $t$ is in seconds. The frequency of the wave in $\mathrm{Hz}$ is
  • $1$
  • B
    $2$
  • C
    $25$
  • D
    $100$
Answer
Correct option: A.
$1$
Here $\omega=2 \pi n=2 \pi \Rightarrow n=1$
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MCQ 231 Mark
The velocity of waves in a string fixed at both ends is $2 \mathrm{~m} / \mathrm{s}$. The string forms standing waves with nodes $5.0 \mathrm{~cm}$ apart. The frequency of vibration of the string in $\mathrm{Hz}$ is
  • A
    $40$
  • B
    $30$
  • $20$
  • D
    $10$
Answer
Correct option: C.
$20$
(c) Here $\frac{\lambda}{2}=5.0 \mathrm{~cm} \Rightarrow \lambda=10 \mathrm{~cm}$
Hence $n=\frac{v}{\lambda}=\frac{200}{10}=20 \mathrm{~Hz}$.
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MCQ 241 Mark
Mechanical waves on the surface of a liquid are
  • A
    Transverse
  • B
    Longitudinal
  • C
    Torsional
  • Both transverse and longitudinal
Answer
Correct option: D.
Both transverse and longitudinal
(d)
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MCQ 251 Mark
At nodes in stationary waves
  • Change in pressure and density are maximum
  • B
    Change in pressure and density are minimum
  • C
    Strain is zero
  • D
    Energy is minimum
Answer
Correct option: A.
Change in pressure and density are maximum
Change in pressure and density are maximum
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MCQ 261 Mark
A string fixed at both the ends is vibrating in two segments. The wavelength of the corresponding wave is
  • A
    $\frac{l}{4}$
  • B
    $\frac{l}{2}$
  • $l$
  • D
    $2 \mathrm{I}$
Answer
Correct option: C.
$l$
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MCQ 271 Mark
Stationary waves of frequency $300 \mathrm{~Hz}$ are formed in a medium in which the velocity of sound is 1200 metre/sec. The distance between a node and the neighbouring antinode is
  • $1 \mathrm{~m}$
  • B
    $2 \mathrm{~m}$
  • C
    $3 \mathrm{~m}$
  • D
    $4 \mathrm{~m}$
Answer
Correct option: A.
$1 \mathrm{~m}$
(a) Required distance $=\frac{\lambda}{4}=\frac{v / n}{4}=\frac{1200}{4 \times 300}=1 \mathrm{~m}$
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MCQ 281 Mark
What is the phase difference between two successive crests in the wave
  • A
    $\pi$
  • B
    $\pi / 2$
  • $2 \pi$
  • D
    $4 \pi$
Answer
Correct option: C.
$2 \pi$
(c) Since distance between two consecutive crests is $\lambda$, so$\phi=\frac{2 \pi}{\lambda} \times \lambda=2 \pi .$
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MCQ 291 Mark
A string is rigidly tied at two ends and its equation of vibration is given by $y=\cos 2 \pi t \sin \sin \pi x$. Then minimum length of string is
  • A
    $1 \mathrm{~m}$
  • $\frac{1}{2} m$
  • C
    $5 \mathrm{~m}$
  • D
    $2 \pi m$
Answer
Correct option: B.
$\frac{1}{2} m$
(b) Given equation of stationary wave is$y=\sin 2 \ \pi x \cos 2 \ \pi t$, comparing it with standard equation
$y=2 A \sin \frac{2 \pi x}{\lambda} \cos \frac{2 \pi x}{\lambda}$
We have $\frac{2 \pi x}{\lambda}=2 \pi x \Rightarrow \lambda=1 \mathrm{~m}$
Minimum distance of string (first mode) $L_{\min }=\frac{\lambda}{2}=\frac{1}{2} m$
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MCQ 301 Mark
Decibel is unit of
  • A
    Intensity of light
  • B
    X-rays radiation capacity
  • Sound loudness
  • D
    Energy of radiation
Answer
Correct option: C.
Sound loudness
(c)
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MCQ 311 Mark
Maximum number of beats frequency heard by a human being is
  • $10$
  • B
    $4$
  • C
    $20$
  • D
    $6$
Answer
Correct option: A.
$10$
(a) Persistence of hearing is $10\  \mathrm{sec}$.
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MCQ 321 Mark
Which of the following do not require medium for transmission
  • A
    Cathode ray
  • Electromagnetic wave
  • C
    Sound wave
  • D
    None of the above
Answer
Correct option: B.
Electromagnetic wave
(b) EM waves do not requires medium for their propagation.
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MCQ 331 Mark
The nature of sound waves in gases is
  • A
    Transverse
  • Longitudinal
  • C
    Stationary
  • D
    Electromagnetic
Answer
Correct option: B.
Longitudinal
(b)
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MCQ 341 Mark
Progressive wave of sound is represented by $y=a \sin [400\  \pi t-\pi x / 6.85]$ where $x$ is in $m$ and $t$ is in sec. Frequency of the wave will be
  • $200 \mathrm{~Hz}$
  • B
    $400 \mathrm{~Hz}$
  • C
    $500 \mathrm{~Hz}$
  • D
    $600 \mathrm{~Hz}$
Answer
Correct option: A.
$200 \mathrm{~Hz}$
(a) $n=\frac{\omega}{2 \pi}=\frac{400 \pi}{2 \pi}=200 \mathrm{~Hz} \quad$ (As $\left.\omega=400 \pi\right)$
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MCQ 351 Mark
If the tension of sonometer's wire increases four times then the fundamental frequency of the wire will increase by
  • $2$ times
  • B
    $4$ times
  • C
    $1 / 2$ times
  • D
    None of the above
Answer
Correct option: A.
$2$ times
$2$ times
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MCQ 361 Mark
The wave length of light in visible part $\left(\lambda_V\right)$ and for sound $\left(\lambda_S\right)$ are related as
  • A
    $\lambda_V<\lambda_S$
  • $\lambda_S>\lambda_V$
  • C
    $\lambda_S=\lambda_V$
  • D
    None of these
Answer
Correct option: B.
$\lambda_S>\lambda_V$
(b)
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MCQ 371 Mark
At what temperature velocity of sound is double than that of at $0^{\circ} \mathrm{C}$
  • A
    $819 K$
  • $819^{\circ} \mathrm{C}$
  • C
    $600^{\circ} \mathrm{C}$
  • D
    $600 K$
Answer
Correct option: B.
$819^{\circ} \mathrm{C}$
$v \propto \sqrt{T} \Rightarrow \frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}} $
$\Rightarrow 2=\sqrt{\frac{T_2}{(273+0)}} $
$\Rightarrow T_2=273\times 4=1092\mathrm{~K}=819^{\circ}\mathrm{C}$
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MCQ 381 Mark
In stationary waves
  • A
    Energy is uniformly distributed
  • Energy is minimum at nodes and maximum at antinodes
  • C
    Energy is maximum at nodes and minimum at antinodes
  • D
    Alternating maximum and minimum energy producing at nodes and antinodes
Answer
Correct option: B.
Energy is minimum at nodes and maximum at antinodes
(b)
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MCQ 391 Mark
Energy is not carried by which of the following waves
  • Stationary
  • B
    Progressive
  • C
    Transverse
  • D
    Electromagnetic
Answer
Correct option: A.
Stationary
(a) Energy is not carried by stationary waves
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MCQ 401 Mark
Fundamental frequency of pipe is $100 \mathrm{~Hz}$ and other two frequencies are $300 \mathrm{~Hz}$ and $500 \mathrm{~Hz}$ then
  • A
    Pipe is open at both the ends
  • B
    Pipe is closed at both the ends
  • One end open and another end is closed
  • D
    None of the above
Answer
Correct option: C.
One end open and another end is closed
One end open and another end is closed
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MCQ 411 Mark
The displacement of the interfering light waves are $y_1=4 \sin \omega t$ and $y_2=3 \sin \left(\omega t+\frac{\pi}{2}\right)$. What is the amplitude of the resultant wave
  • $5$
  • B
    $7$
  • C
    $1$
  • D
    $0$
Answer
Correct option: A.
$5$
(a) Since $\phi=\frac{\pi}{2} \Rightarrow A=\sqrt{a_1^2+a_2^2}=\sqrt{(4)^2+(3)^2}=5$
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MCQ 421 Mark
Two sirens situated one kilometer apart are producing sound of frequency $330 \mathrm{~Hz}$. An observer starts moving from one siren to the other with a speed of $2 \mathrm{~m} / \mathrm{s}$. If the speed of sound be $330 \mathrm{~m} / \mathrm{s}$, what will be the beat frequency heard by the observer
  • A
    8
  • 4
  • C
    6
  • D
    1
Answer
Correct option: B.
4
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MCQ 431 Mark
Two waves are represented by $y_1=a \sin \left(\omega t+\frac{\pi}{6}\right)$ and $y_2=a \cos \omega t$. What will be their resultant amplitude
  • $a$
  • B
    $\sqrt{2} a$
  • C
    $\sqrt{3} a$
  • D
    $2 a$
Answer
Correct option: A.
$a$
(c) $A=\sqrt{\left(a_1^2+a_2^2+2 a_1 a_2 \cos \phi\right)}$Putting $a_1=a_2=a$ and $\phi=\frac{\pi}{3}$, we get $A=\sqrt{3} a$
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MCQ 441 Mark
At what speed should a source of sound move so that stationary observer finds the apparent frequency equal to half of the original frequency
  • A
    $\frac{v}{2}$
  • B
    $2 v$
  • C
    $\frac{v}{4}$
  • $v$
Answer
Correct option: D.
$v$
(d) Frequency is decreasing (becomes half), it means source is going away from the observes. In this case frequency observed by the observer is$n^{\prime}=n\left(\frac{v}{v+v_S}\right) \Rightarrow \frac{n}{2}=n\left(\frac{v}{v+v_S}\right) \Rightarrow v_S=v$
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MCQ 451 Mark
A student determines the velocity of sound with the help of a closed organ pipe. If the observed length for fundamental frequency is $24.7 \ m$, the length for third harmonic will be
  • $74.1 \mathrm{~cm}$
  • B
    $72.7 \mathrm{~cm}$
  • C
    $75.4 \mathrm{~cm}$
  • D
    $73.1 \mathrm{~cm}$
Answer
Correct option: A.
$74.1 \mathrm{~cm}$
(a) $l_2=3 l_1=3 \times 24.7=74.1 \mathrm{~cm}$
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MCQ 461 Mark
Velocity of sound measured in hydrogen and oxygen gas at a given temperature will be in the ratio
  • A
    $1: 4$
  • $4: 1$
  • C
    $2: 1$
  • D
    $1: 1$
Answer
Correct option: B.
$4: 1$
$v _{ h } \propto \frac{1}{m_{ h }} \text { and } v _{ o } \propto \frac{1}{m_{ o }}$
$\Rightarrow \frac{ v _{ h }}{ v _{ o }}=\sqrt{\frac{ m _0}{m_{ h }}} $
$\therefore \frac{ v _{ h }}{ v _{ o }}=\sqrt{\frac{16}{1}}$
$\therefore \frac{ v _{ h }}{ v _{ o }}=\frac{4}{1}$
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MCQ 471 Mark
To increase the frequency from $100 \mathrm{~Hz}$ to $400 \mathrm{~Hz}$ the tension in the string has to be changed by
  • A
    $4$ times
  • $16$ times
  • C
    $20$ times
  • D
    None of these
Answer
Correct option: B.
$16$ times
$16$ times
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MCQ 481 Mark
If source and observer both are relatively at rest and if speed of sound is increased then frequency heard by observer will
  • A
    Increases
  • B
    Decreases
  • C
    Can not be predicted
  • Will not change
Answer
Correct option: D.
Will not change
(d) No change in frequency.
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MCQ 491 Mark
Speed of sound at constant temperature depends on
  • A
    Pressure
  • B
    Density of gas
  • C
    Above both
  • None of the above
Answer
Correct option: D.
None of the above
(d) Speed do sound, doesn't depend up on pressure and density medium.
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MCQ 501 Mark
Sound waves in air are
  • A
    Transverse
  • Longitudinal
  • C
    De-Broglie waves
  • D
    All the above
Answer
Correct option: B.
Longitudinal
(b) Because sound waves in gases are longitudinal.
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