MCQ 11 Mark
A stretched string, $2 m$ long, vibrates in its third overtone. The distance between consecutive nodes is
- A
$40 cm$
- ✓
$50 cm$
- C
$66.7 cm$
- D
$100 cm$.
AnswerCorrect option: B. $50 cm$
$50 cm$
View full question & answer→MCQ 21 Mark
Two vibrating particles in the adjacent loops of a stationary wave have ..... at a given instant.
- A
- ✓
- C
slightly different phases
- D
View full question & answer→MCQ 31 Mark
At a given instant two vibrating particles in the same loop of a stationary wave have
- ✓
- B
- C
slightly different phases
- D
View full question & answer→MCQ 41 Mark
Two simple harmonic waves of the same amplitude and frequency, but $90^{\circ}$ out of phase, pass through the same region in a medium. The resultant wave has
- ✓
an amplitude greater than either of the component waves
- B
an amplitude smaller than either of the component waves
- C
- D
an amplitude slowly varying with time.
AnswerCorrect option: A. an amplitude greater than either of the component waves
an amplitude greater than either of the component waves
View full question & answer→MCQ 51 Mark
A transverse wave travelling in a denser medium is reflected from a rarer medium. Then,
AnswerCorrect option: A. an incident crest is reflected as a crest
an incident crest is reflected as a crest
View full question & answer→MCQ 61 Mark
When a longitudinal wave is incident at the boundary of a denser medium, then
- ✓
a compression reflects as a compression
- B
a compression reflects as a rarefaction
- C
a rarefaction reflects as a compression
- D
a longitudinal wave reflects as a transverse wave.
AnswerCorrect option: A. a compression reflects as a compression
a compression reflects as a compression
View full question & answer→MCQ 71 Mark
If two sound waves with the same amplitude but slightly different frequencies $n_1$ and $n_2$ superpose to produce beats, the resultant wave motion has frequency
AnswerCorrect option: D. $\frac{n_1+n_2}{2}$
$\frac{n_1+n_3}{2}$
View full question & answer→MCQ 81 Mark
In a set of 25 tuning forks, arranged in order of increasing frequency, each fork gives 3 beats per second with the succeeding one. If the frequency of the 10th fork is $127 Hz$, the frequency of the 16 th fork is
- A
$139 Hz$
- ✓
$145 Hz$
- C
$148 Hz$
- D
$151 Hz$.
AnswerCorrect option: B. $145 Hz$
$145 Hz$
View full question & answer→MCQ 91 Mark
A tuning fork gives 1 beat in 2 seconds with a timing fork of frequency $341.3 Hz$. If the beat: frequency decreases when the first fork is filed a little, its original frequency was
- A
$336.3 Hz$
- ✓
$340.8 Hz$
- C
$341.8 Hz$
- D
$346.3 Hz$.
AnswerCorrect option: B. $340.8 Hz$
$340.8 Hz$
View full question & answer→MCQ 101 Mark
A tuning fork $A$ of frequency $512 Hz$ produces 3 beats per second with another tuning fork $B$ of frequency $515 Hz$. If the prongs of $B$ are filed a little, the number of beats produced per second will
View full question & answer→MCQ 111 Mark
The equation of a progressive wave is $y=7 \sin (4 t-0.02 x)$, where $x$ and $y$ are in centimetre and time $t$ in second. The maximum velocity of a particle is
- ✓
$28 cm / s$
- B
$32 cm / s$
- C
$49 cm / s$
- D
$112 cm / s$.
AnswerCorrect option: A. $28 cm / s$
$28 cm / s$
View full question & answer→MCQ 121 Mark
In the formation of beats, the resultant amplitude varies with a frequency equal to
- A
- B
- ✓
- D
double the beat frequency.
View full question & answer→MCQ 131 Mark
Let $n_1$ and $n_2$ be two slightly different frequencies of sound waves. The time interval between a waxing and the immediate next waning is
AnswerCorrect option: D. $\frac{1}{2\left(n_1-n_2\right)}$
$\frac{1}{2\left(n_1-n_1\right)}$
View full question & answer→MCQ 141 Mark
One beat means that the intensity of sound should be
- A
- B
- ✓
once maximum and once minimum
- D
twice maximum and twice minimum.
AnswerCorrect option: C. once maximum and once minimum
once maximum and once minimum
View full question & answer→MCQ 151 Mark
When the air column in a pipe closed at one end vibrates such that three nodes are formed in it, the frequency of its vibrations is…..times the fundamental frequency.
MCQ 161 Mark
The frequency of the second overtone of the vibration of a stretched string is
- A
$\frac{1}{l} \sqrt{\frac{T}{m}}$
- ✓
$\frac{3}{2 l} \sqrt{\frac{T}{m}}$
- C
$\frac{1}{2l} \sqrt{\frac{T}{m}}$
- D
$\frac{2}{3l} \sqrt{\frac{T}{m}}$
AnswerCorrect option: B. $\frac{3}{2 l} \sqrt{\frac{T}{m}}$
$\frac{3}{2l} \sqrt{\frac{T}{m}}$
View full question & answer→MCQ 171 Mark
Velocity of a transverse wave along a stretched string is proportional to IT = tension in the string]
- ✓
$\sqrt{T}$
- B
$T$
- C
$\frac{1}{\sqrt{T}}$
- D
$\frac{1}{T}$
AnswerCorrect option: A. $\sqrt{T}$
$\sqrt{T}$
View full question & answer→MCQ 181 Mark
A sonometer wire vibrates with three nodes and two antinodes. The corresponoling mode of vibration is
MCQ 191 Mark
In an open organ pipe, the first overtone produced is of such frequency that the length of the pipe is equal to
- A
$\frac{\lambda}{4}$
- B
$\frac{\lambda}{3}$
- C
$\frac{\lambda}{2}$
- ✓
$\lambda$
AnswerCorrect option: D. $\lambda$
$\lambda$
View full question & answer→MCQ 201 Mark
Of two long narrow organ pipes $A$ and $B, A$ is open at one end and $B$ at both ends. If both the pipes have the same fundamental frequency, the first overtone of $A$ is the first overtone of $B$.
AnswerCorrect option: B. $\frac{2}{3}$ of
$\frac{2}{3}$ of
View full question & answer→MCQ 211 Mark
The value of end correction for an open organ pipe of radius $r$ is
- A
$0.3 r$
- B
$0.6 r$
- C
$0.9 r$
- ✓
$1.2 r$.
AnswerCorrect option: D. $1.2 r$.
$1.2 r$.
View full question & answer→MCQ 221 Mark
What is the period of the wave given by $y=0.003 \sin \left(\frac{\pi}{0.08} t+\frac{\pi}{8} x\right)$ (in SI units) ?
- A
$0.08 s$
- ✓
$0.16 s$
- C
$0.32 s$
- D
$0.8 s$.
AnswerCorrect option: B. $0.16 s$
$0.16 s$
View full question & answer→MCQ 231 Mark
Of two narrow organ pipes $A$ and $B, A$ is open at one end and $B$ at both ends. Both the pipes have the same fundamental frequency. If $A$ is $1.2 m$ long, how long is $B$ ?
- A
$0.8 m$
- B
$1.8 m$
- ✓
$2.4 m$
- D
$3.0 m$
AnswerCorrect option: C. $2.4 m$
$2.4 m$
View full question & answer→MCQ 241 Mark
An organ pipe is closed at one end. The pth overtone is the….th harmonic.
- ✓
$2 p+1$
- B
$2 p-1$
- C
$p+1$
- D
$P-1$
AnswerCorrect option: A. $2 p+1$
$2 p+1$
View full question & answer→MCQ 251 Mark
Two strings, $A$ and $B$, have the same tension and length. The string $A$ has a mass $m$ while the string $B$ has a mass Am. If the speed of the waves in string $A$ is $v$, that on string $B$ is
- ✓
$\frac{1}{2} v$
- B
$v$
- C
$2 v$
- D
$v$,
AnswerCorrect option: A. $\frac{1}{2} v$
$\frac{1}{2} v$
View full question & answer→MCQ 261 Mark
Two strings $A$ and $B$ are identical except that the diameter of $A$ is twice the diameter of $B$. The ratio of the frequency of sound from $A$ to that from $B$ is
- A
$2: 1$
- B
$\sqrt{2}: 1$
- C
$1: \sqrt{2}$
- ✓
$1: 2$.
AnswerCorrect option: D. $1: 2$.
$1: 2$.
View full question & answer→MCQ 271 Mark
A stretched string of length $50 cm$ vibrates in five segments when stationary waves are formed on it. If the wave speed is $14 m / s$, its frequency of vibration is
- A
$28 Hz$
- B
$35 Hz$
- ✓
$70 Hz$
- D
$140 Hz$.
AnswerCorrect option: C. $70 Hz$
$70 Hz$
View full question & answer→MCQ 281 Mark
The fundamental frequency of transverse vibrations of a stretched string of radius $r$ is proportional to
- A
$r^{-2}$
- ✓
$r^{-1}$
- C
$r^{-\frac{1}{2}}$
- D
$r^2$
AnswerCorrect option: B. $r^{-1}$
$r^{-1}$
View full question & answer→MCQ 291 Mark
Stationary waves are produced on a $10 m$ long stretched string fixed at both ends. If the string vibrates in 5 segments and the wave velocity is $20 m / s$, the frequency of the waves is
- A
$10 Hz$
- ✓
$5 Hz$
- C
$4 Hz$
- D
$2 Hz$.
AnswerCorrect option: B. $5 Hz$
$5 Hz$
View full question & answer→MCQ 301 Mark
A travelling wave of frequency $100 Hz$ along a string is reflected from a fixed end. The stationary wave formed has the nearest node at a distance of $10 cm$ from the fixed end. The speed of the travelling wave was
- A
$40 m / s$
- ✓
$20 m / s$
- C
$10 m / s$
- D
$5 m / s$.
AnswerCorrect option: B. $20 m / s$
$20 m / s$
View full question & answer→MCQ 311 Mark
A stretched string tied between two rigid supports vibrates with a frequency double the fundamental frequency. The point midway between the supports is
- ✓
- B
- C
either a node or an antinode
- D
neither a node nor an antinode.
View full question & answer→MCQ 321 Mark
A stretched string of length I vibrates in the third overtone. The wavelength of stationary wave formed is
- ✓
$\frac{l}{2}$
- B
$\frac{l}{4}$
- C
- D
AnswerCorrect option: A. $\frac{l}{2}$
$\frac{l}{2}$
View full question & answer→MCQ 331 Mark
A simple harmonic wave of frequency $20 Hz$ is travelling in the positive direction of $x$-axis with a velocity of $30 m / s$. Two particles in the path of the wave, $0.45 m$ apart, differ in phase by
- A
$\frac{\pi}{3} rad$
- B
$\frac{\pi}{2} rad$
- ✓
$0.6 \pi rad$
- D
$\pi rad$.
AnswerCorrect option: C. $0.6 \pi rad$
$0.6 \pi rad$
View full question & answer→MCQ 341 Mark
A standing wave is produced on a string fixed at one end with the other end free. The length of the string
- ✓
must be an odd integral multiple of λ/4.
- B
must be an odd integral multiple of λ/2.
- C
must be an odd integral multiple of λ.
- D
must be an even integral multiple ofλ.
AnswerCorrect option: A. must be an odd integral multiple of λ/4.
must be an odd integral multiple of λ/4.
View full question & answer→MCQ 351 Mark
Which of the following equations represents a wave travelling along the y-axis?
MCQ 361 Mark
The tension in a piano wire is increased by 25%. Its frequency becomes ….. times the original frequency.
MCQ 371 Mark
If two open organ pipes of length 50 cm and 51 cm sounded together produce 7 beats per second, the speed of sound is.
MCQ 381 Mark
When an air column in a pipe closed at one end vibrates such that three nodes are formed in it, the frequency of its
vibrations is …….times the fundamental frequency.
MCQ 391 Mark
The equation of simple harmonic progressive wave is given by $y=a \sin 2 \pi(b t-c x)$.The maximum particle velocity will be half the wave velocity if $c=$
- A
$2 \pi a$
- ✓
$\frac{1}{4 \pi a}$
- C
$\frac{1}{2 \pi a}$
- D
$4 \pi a$
AnswerCorrect option: B. $\frac{1}{4 \pi a}$
(b) : $y=a \sin 2 \pi(b t-c x)$
comparing with, $y=A \sin (\omega t-k x)$
$
\omega=2 \pi b, k=2 \pi c
$
Maximum particle velocity $=\omega A$...(i)
Wave velocity, $v=\frac{\omega}{k}$...(ii)
$
\begin{aligned}
& v_{\text {max }}=\frac{1}{2} v_{\text {Wave }} ; \omega a=\frac{1}{2} \cdot \frac{\omega}{k} \\
& a=\frac{1}{2} \times \frac{1}{2 \pi c} \Rightarrow c=\frac{1}{4 \pi a}
\end{aligned}
$
View full question & answer→MCQ 401 Mark
If the end correction of an open pipe is $0.8 cm$, then the inner radius of that pipe is
- A
$\frac{1}{3} cm$
- ✓
$\frac{2}{3} cm$
- C
$\frac{3}{2} cm$
- D
$0.2 cm$
AnswerCorrect option: B. $\frac{2}{3} cm$
(b) : End correction of an open pipe,
$
e_{\text {opct }}=0.8 cm
$
End correction on each side, $e=\frac{e_{\text {open }}}{2}=\frac{0.8}{2}=0.4 cm$ Diameter of inner part of pipe, $D=\frac{e}{0.3}=\frac{0.4}{0.3} cm$
Radius of inner part of the pipe, $r=\frac{D}{2}=\frac{4}{3 \times 2}=\frac{2}{3} cm$
View full question & answer→MCQ 411 Mark
Stationary waves can be produced in
- A
only solid and gaseous media
- B
only liquid and gaseous media
- C
only solid and liquid media
- ✓
solid, liquid and gaseous media.
AnswerCorrect option: D. solid, liquid and gaseous media.
(d) solid, liquid and gaseous media.
View full question & answer→MCQ 421 Mark
If the length of an open organ pipe is $33.3 cm$, then the frequency of fifth overtone is [Neglect end correction, velocity of sound $=333 m / s$ ]
- A
$3500 Hz$
- ✓
$3000 Hz$
- C
$2500 Hz$
- D
$2000 Hz$
AnswerCorrect option: B. $3000 Hz$
(b) : Given, $L=33.3 cm , v=333 m / s$
For open organ pipe, for $n=1$
$
\begin{aligned}
& \lambda_1=\frac{2 L}{n}=\frac{2 L}{1} \Rightarrow L=\frac{\lambda_1}{2} \\
& f_1=\frac{v}{\lambda_1}=\frac{v}{2 L}
\end{aligned}
$
It is called fundamental frequency.
For $n=2, f_2=\frac{2 v}{2 L}=2 f_1$
For $n=3, f_3=\frac{3 v}{2 L}=3 f_1$
For $n=6$, (fifth overtone)
$
f_6=6 \times f_1=6 \times \frac{v}{2 L}=\frac{6 \times 333}{2 \times 33.3 \times 10^{-2}}=3000 Hz
$
View full question & answer→MCQ 431 Mark
A closed organ pipe length ' $L_1$ ' and an open organ pipe contain diatomic gases of densities ' $\rho_1$ ' and ' $\rho_2$ ' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)
- A
$\frac{4 L_1}{3}$
- ✓
$\frac{4 L_1}{3} \sqrt{\frac{\rho_1}{\rho_2}}$
- C
$\frac{4 L_1}{3} \sqrt{\frac{\rho_2}{\rho_1}}$
- D
$\frac{3}{4 L_1} \sqrt{\frac{\rho_1}{\rho_2}}$
AnswerCorrect option: B. $\frac{4 L_1}{3} \sqrt{\frac{\rho_1}{\rho_2}}$
(b) : Frequency of $I ^{ st }$ overtone of closed pipe $=\frac{3 v}{4 L_1}$ Frequency of $I ^{-1}$ overtone of open pipe $=\frac{v}{L_2}$
$
\begin{aligned}
& \frac{3 v}{4 L}=\frac{v}{L_2} ; \frac{3}{4 L_1} \sqrt{\frac{\gamma P}{\rho_1}}=\frac{1}{L_2} \sqrt{\frac{\gamma P}{\rho_2}} ; \\
& L_2=\frac{4 L_1}{3} \sqrt{\frac{\rho_1}{\rho_2}}=\frac{4 L_1}{3} \sqrt{\frac{\rho_1}{\rho_2}}
\end{aligned}
$
View full question & answer→MCQ 441 Mark
When a string of length $l$ is divided into three segments of length $l_1, l_2$ and $l_3$. The fundamental frequencies of three segments are $n_1, n_2$ and $n_3$ respectively. The original fundamental frequency $' n\ ' $of the string is
- A
$n=n_1+n_2+n_3$
- B
$\sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}$
- ✓
$\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
- D
$\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$
AnswerCorrect option: C. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
$n=\frac{1}{2 l} \sqrt{\frac{T}{m}} ;$
$n_1 l_1=n_2 l_2=n_3 l_3=K$
So, $l_1=\frac{K}{n_1}, l_2=\frac{K}{n_2},$
$l_3=\frac{K}{n_3} ;$
$l=\frac{K}{n}$
$l=l_1+l_2+l_3$
$\frac{K}{n}=\frac{K}{n_1}+\frac{K}{n_2}+\frac{K}{n_3} ;$
$\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
View full question & answer→MCQ 451 Mark
A sonometer wire $49 cm$ long is in unison with a tuning fork of frequency ' $n$ '. If the length of the wire is decreased by $1 cm$ and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of ' $n$ ' is
- A
$256 Hz$
- ✓
$288 Hz$
- C
$320 Hz$
- D
$384 Hz$
AnswerCorrect option: B. $288 Hz$
(b) : Given, $l=49 cm$, beats $=6 / sec$
$
\begin{aligned}
& n=\frac{1}{2 l} \sqrt{\frac{T}{m}} \\
& n=\frac{100}{2 \times 49} \sqrt{\frac{T}{m}} ...(i)\\
& n+6=\frac{100}{2 \times 48} \sqrt{\frac{T}{m}}....(ii)
\end{aligned}
$
By equation (i) and (ii), $\frac{n}{n+6}=\frac{100 \times 2 \times 48}{2 \times 49 \times 100}$
$
49 n=48 n+48 \times 6 ; n=288 Hz
$
View full question & answer→MCQ 461 Mark
A wire $P Q$ has length $4.8 m$ and mass $0.06 kg$. Another wire $Q R$ has length $2.56 m$ and mass $0.2 kg$. Both wires have same radii and are joined as a single wire. This wire is under tension of $80 N$. A wave pulse of amplitude $3.5 cm$ is sent along the wire $P Q$ from end $P$. The time taken by the wave to reach the other end of single wire is (No power is dissipated during propagation)
- A
$0.1 s$
- B
$0.12 s$
- ✓
$0.14 s$
- D
$0.16 s$
AnswerCorrect option: C. $0.14 s$
(c) : Amplitude, $A=3.5 cm , T =80 N$
$
\mu_{P Q}=\frac{0.06}{4.8}=0.0125 kg / m ; \quad \mu_{Q R}=\frac{0.2}{2.56}=0.0781 kg / m
$
$\begin{aligned} & v_{P Q}=\sqrt{\frac{T}{\mu_{P Q}}}=\sqrt{\frac{80}{0.0125}}=80 m / s ; \quad t_{P Q}=\frac{4.8}{80}=0.06 sec \\ & v_{Q R}=\sqrt{\frac{T}{\mu_{Q R}}}=\sqrt{\frac{80}{0.0781}}=32.01 m / s \\ & t_{Q R}=\frac{2.56}{32.01}=0.08 sec \\ & t=t_{P Q}+t_{Q R}=0.06+0.08=0.14 s \end{aligned}$
View full question & answer→MCQ 471 Mark
If ' $T$ ' is the length of the open pipe, ' $r$ ' is the internal radius of the pipe and ' $V$ ' is the velocity of sound in air then fundamental frequency of open pipe is
- A
$\frac{V}{(1+0.3 r)}$
- B
$\frac{V}{(l+1.2 r)}$
- C
$\frac{V}{(l+0.6 r)}$
- ✓
$\frac{V}{2(l+1.2 r)}$
AnswerCorrect option: D. $\frac{V}{2(l+1.2 r)}$
(d) : $f_0=\frac{V}{2(l+1.2 r)}$
View full question & answer→MCQ 481 Mark
A string is stretched between two rigid supports separated by $75 cm$. There are no resonant frequencies between $420 Hz$ and $315 Hz$. The lowest resonant frequency for the string is
- A
$210 Hz$
- B
$180 Hz$
- ✓
$105 Hz$
- D
$1050 Hz$
AnswerCorrect option: C. $105 Hz$
(c) : Let $315 Hz$ be the $n^{\text {th }}$ harmonic of the string
$So _1, \frac{n v}{2 l}=315$....(i)
$
\frac{(n+1) v}{n}=420..(ii)
$
Dividing equation (ii) by (i),
$
\begin{aligned}
& \therefore \quad \frac{(n+1) v}{n}=420 \\
& 315 n+315=420 n \Rightarrow n=3 \\
& \text { So, lowest frequency }=\frac{v}{2 l}=\frac{315}{n}=105 Hz
\end{aligned}
$
View full question & answer→MCQ 491 Mark
The displacement of a wave travelling in the $x$ direction is $y=10^{-4} \sin \left[600 t-2 x+\frac{\pi}{3}\right] m$, where $x$ is in metre and $t$ in second. The speed of the wave is
- ✓
$300 m / s$
- B
$200 m / s$
- C
$150 m / s$
- D
$600 m / s$
AnswerCorrect option: A. $300 m / s$
(a) : The given equation,
$
y=10^{-4} \sin \left[600 t-2 x+\frac{\pi}{3}\right] m
$
On comparing this equation with standard equation with $y=A \sin (\omega t-k x)$, we get
$
\begin{aligned}
& \omega=600 ; k=2 \\
& v=\frac{\omega}{k}=\frac{600}{2}=300 m / s
\end{aligned}
$
View full question & answer→MCQ 501 Mark
Forastationary wave, $Y=10 \sin \left(\frac{\pi x}{15}\right) \cos (48 \pi t ) cm$, the distance between a node and the successive antinode is
- A
$60 cm$
- B
$30 cm$
- ✓
$7.5 cm$
- D
$15 cm$
AnswerCorrect option: C. $7.5 cm$
(c) : On comparing the given equation with a standard stationary wave equation, we get
$
k=\frac{\pi}{15}=\frac{2 \pi}{\lambda} \Rightarrow \lambda=30 cm
$
Distance between node and antinode is, $\frac{\lambda}{4}=\frac{30}{4}=7.5 cm$
View full question & answer→