Waves Test

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Waves Test - 61

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Weekly Quiz Competition

Question 1
1 / -0

A particle performs simple harmonic motionwith amplitude A. Its speed is trebled at the instant when it is at a distance $\dfrac { 2 \mathrm { A } } { 3 }$ fromequilibrium position. Find the new amplitudeof the motion.

A
$\dfrac { 7 \mathrm { A } } { 3 }$

B
$\dfrac { \mathrm { A } } { 3 } \sqrt { 41 }$

C
3 $\mathrm { A }$

D
$\mathrm { A } \sqrt { 3 }$
Question 2
1 / -0

A sound wave travels at a speed of $330m/s.$ If the wavelength is $1.56cm$ what is the frequency of the wave? will it be audible for human

A
$50Hz$

B
$30Hz$

C
$20Hz$

D
$45Hz$

Solution

$s=330$
$h=1.5cm=1.5/100=0.015$
$s×h$
$330×0.015$
$=4.95 Hz$
it Will not be audible as it less than $20Hz$
Hence,
option $(C)$ is correct answer.
Question 3
1 / -0

A particle in S.H.M. is described by the displacement function $x(t) = a cos(ax + \theta)$ . If the initial (t = 0) position of the particle is 1 cm and its initial velocity is $\pi cm/s$ . The angular frequency of the particle is $\pi rad /s$ ,then it's amplitude is

A
1 cm

B
$\sqrt{2}cm$

C
2 cm

D
2.5 cm

Solution

$\begin{array}{l} Given, \\ Diplacement\, \, function\, \, of\, \, the\, \, particle\, \, is, \\ x\left( t \right) =A\cos \left( { \omega t+\phi } \right) \\ x\left( 0 \right) =1\, \, cm\, \, and\, \, \, v\left( 0 \right) \, \, =\pi \, \, \dfrac { { cm } }{ { \sec } } \\ differentiating\, \, w.r.\, \, to\, \, t, \\ v\left( t \right) =-A\left( \omega \right) \sin \left( { \omega t+\varphi } \right) ..........\left( 1 \right) \\ At\, \, t=0, \\ x\left( 0 \right) =A\omega \sin \left( \phi \right) ..........\left( 2 \right) \\ v\left( 0 \right) =-A\omega \sin \left( \phi \right) ............\left( 3 \right) \\ Dividing\, \, \left( 3 \right) \, \, by\, \, \left( 2 \right) , \\ \dfrac { { v\left( 0 \right) } }{ { x\left( 0 \right) } } =-\omega \tan \phi \\ \Rightarrow \pi =-\omega \tan \phi \\ \Rightarrow \tan \phi =-1 \\ i.e\, \, \, \phi =\dfrac { { 3\pi } }{ 4 } \, \, or\, \, \dfrac { { 7\pi } }{ 4 } \\ \sin ce\, \, ,at\, \, \, t=0 \\ x\left( 0 \right) =A\cos \left( \phi \right) =1 \\ \Rightarrow \cos \phi \, \, \, is\, \, \, positive. \\ Therefore\, \, ,\phi =\dfrac { { 7\pi } }{ 4 } \\ \therefore A\cos \left( { \dfrac { { 7\pi } }{ 4 } } \right) =1 \\ \Rightarrow A=\sqrt { 2 } \, \, cm \end{array}$
Question 4
1 / -0

Consider the following two equations
A) $L=I\omega$ and
B) $\dfrac { dL }{ dt } =\Gamma$ . In noninertial frames :

A
both A and B are true

B
A is true but B is false

C
B is true but A is false

D
both A and B are false.
Solution
Angular momentum $L = Iw$
A rigid object's angular momentum is stated as follows :
The cross product of the moment of inertia and angular velocity.
It is considered as analogous to corresponding linear momentum.
If there are no other external torque acts on the object, it is subject to the basic limitations of the angular momentum theory.
$\dfrac{dL}{dt}$ = Total external force torque not equal to any torque.

So, $\dfrac{dL}{dt}$ = Γ is not correct.

Hence, option (b) A is true but B is false.
Question 5
1 / -0

If x= $\theta sin(\alpha + \dfrac{\pi}{6})$ and $x^1 = {\theta}cos\alpha$ ,then what is the phase difference between the two waves.

A
$\pi/3$

B
$\pi/6$

C
$\pi/2$

D
$\pi$
Question 6
1 / -0

The phase (at a time t) of a particle in simple harmonic motion tells

A
Only the position of the particle at time t

B
Only the direction of motion of the particle at time t

C
Both the position and direction of motion of the particle at time t

D
Neither the position of the particle nor its direction of motion at time t
Question 7
1 / -0

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2\times { 10 }^{ -2 }\cos { \pi t }$ meters. The time at which the maximum speed first occurs is :

A
$0.5 s$

B
$0.75 s$

C
$0.125 s$

D
$0.25 s$
Question 8
1 / -0

A particle executes a SHM of time T, find the time taken by the particle to go directly from its mean position to half the amplitude

A
$\dfrac{T}{2}$

B
$\dfrac{T}{8}$

C
$\dfrac{T}{12}$

D
$\dfrac{T}{4}$

Solution
Question 9
1 / -0

A boat has green light of wavelength $\lambda= 500nm$ on the MAST. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat?
Given $\eta_{w} = 4/3$

A
Green of wavelength $500 nm$

B
Blue of wavelength $376nm$

C
Green of wavelength $375 nm$

D
Red of wavelength $665 nm$
Question 10
1 / -0

Speed of wave 'v' is given by

A
Wavelength of the wave / frequency of the wave

B
Wavelength of the wave $\times$ frequency of the wave

C
frequency of the wave/Wavelength of the wave

D
None of these

Solution

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Waves Test - 61

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Waves Test - 61

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Question 1

7A3\dfrac { 7 \mathrm { A } } { 3 }37A​

A341\dfrac { \mathrm { A } } { 3 } \sqrt { 41 }3A​41​

3A\mathrm { A }A

A3\mathrm { A } \sqrt { 3 }A3​

Question 2

50Hz50Hz50Hz

30Hz30Hz30Hz

20Hz20Hz20Hz

45Hz45Hz45Hz

Solution

Question 3

1 cm

2cm\sqrt{2}cm2​cm

2 cm

2.5 cm

Solution

Question 4

both A and B are true

A is true but B is false

B is true but A is false

both A and B are false.

Solution

Question 5

π/3\pi/3π/3

π/6\pi/6π/6

π/2\pi/2π/2

π\piπ

Question 6

Only the position of the particle at time t

Only the direction of motion of the particle at time t

Both the position and direction of motion of the particle at time t

Neither the position of the particle nor its direction of motion at time t

Question 7

0.5s0.5 s0.5s

0.75s0.75 s0.75s

0.125s0.125 s0.125s

0.25s0.25 s0.25s

Question 8

T2\dfrac{T}{2}2T​

T8\dfrac{T}{8}8T​

T12\dfrac{T}{12}12T​

T4\dfrac{T}{4}4T​

Solution

Question 9

Green of wavelength 500nm500 nm500nm

Blue of wavelength 376nm376nm376nm

Green of wavelength 375nm375 nm375nm

Red of wavelength 665nm665 nm665nm

Question 10

Wavelength of the wave / frequency of the wave

Wavelength of the wave ×\times × frequency of the wave

frequency of the wave/Wavelength of the wave

None of these

Solution

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$\dfrac { 7 \mathrm { A } } { 3 }$

$\dfrac { \mathrm { A } } { 3 } \sqrt { 41 }$

3 $\mathrm { A }$

$\mathrm { A } \sqrt { 3 }$

$50Hz$

$30Hz$

$20Hz$

$45Hz$

$\sqrt{2}cm$

$\pi/3$

$\pi/6$

$\pi/2$

$\pi$

$0.5 s$

$0.75 s$

$0.125 s$

$0.25 s$

$\dfrac{T}{2}$

$\dfrac{T}{8}$

$\dfrac{T}{12}$

$\dfrac{T}{4}$

Green of wavelength $500 nm$

Blue of wavelength $376nm$

Green of wavelength $375 nm$

Red of wavelength $665 nm$

Wavelength of the wave $\times$ frequency of the wave