Waves Test

Result

Waves Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

Two waves of the same amplitude and frequency arrive at a point simultaneously. what should the phase difference between the waves so that amplitude of the resultant wave is double(2A)

A
$$\dfrac {\pi}{2} radian$$

B
$$\dfrac {2\pi}{3} radian$$

C
$$\dfrac {3\pi}{4} radian$$

D
zero

Solution
Question 2
1 / -0

The wavelength of the wave is:

A
$$6 \ cm$$

B
$$24 \ cm$$

C
$$12 \ cm$$

D
$$16 \ cm$$

Solution

(Refer to Image)
A simple harmonic plane along $$x$$ axis in a medium
For $$x=0$$ (curve 1)
and $$x=7$$ (curve 2)
The two particles are within a span of the wavelength= ?
$$\lambda= \cfrac {2 \Pi}{T}$$
or, $$\lambda= \cfrac {2\Pi}{\cfrac {7}{400}-\cfrac {1}{400}}=12 cm$$ .
Question 3
1 / -0

A body executing S.H.M has a maximum acceleration equal to $$48$$ m$$/\sec^2$$ and maximum velocity equal to $$12$$ m/$$\sec$$. The amplitude of S.H.M is?

A
$$3$$ m

B
$$3/32$$ m

C
$$1024/9$$ m

D
$$64/9$$ m

Solution

Form maximum velocity $$\text{ v }_{ max }=\quad A\omega ;$$=12 m/s
and from maximum acceleration $$\text{ a }_{ max }=\quad A{ \omega }^{ 2 }$$=48 $$m/{ s }^{ 2 }$$
where A is the amplitude of SHM.
Putting the value of $$\omega$$=$$\dfrac { 12 }{ A } $$ in maximum acceleration we get ,
$$\dfrac { 144 }{ { A }^{ 2 } } \times A=48\\ A=\dfrac { 144 }{ 48 } =3\quad \quad $$ m
Question 4
1 / -0

A nylon guitar string has a linear density of $$7.20\ g/m$$ and is under tension of $$150\ N$$. The fixed supports are distance $$D= 90.0\ cm$$ apart. The string is oscillating in the standing wave pattern shown in figure.Calculate the
(ii) The wavelength of the traveling waves whose superposition gives this standing wave.

A
20 cm

B
40.0 cm

C
60.0 cm

D
80.0 cm
Question 5
1 / -0

A sine wave is travelling in a medium. A particular particle has zero displacement at a certain instant. the particle closest to it having zero displacement is at a distance

A
$$\lambda/4$$

B
$$\lambda/3$$

C
$$\lambda/2$$

D
$$\lambda$$

Solution

The minima of the sine wave function occurs at 0 and after this, the next minima of the sine wave occurs at $$\pi$$. The wavelength of the sine wave function is $$2\pi$$ i.e. one wave completes its full waveform in period of $$2\pi$$.
then the particle closest to it having zero displacement is at a distance $$\pi$$ and is equal to $$\lambda/2$$
Question 6
1 / -0

A particle performing simple harmonic motion along x-axis, with $$x = 0$$ as the mean position is released from rest at $$x = 2 cm$$ at $$t = 0$$. The time taken by particle in crossing the position $$x = 1.6cm$$ for the second time is: [Take amplitude of simple harmonic motion as $$2cm$$ and its period as $$1s$$]

A
$$\dfrac{1}{12}s$$

B
$$\dfrac{11}{12}s$$

C
$$\dfrac{323}{360}s$$

D
$$\dfrac{23}{66}s$$
Question 7
1 / -0

A particle moves along the X-axis according to the equation $$x = 10{\sin ^3}(\pi t)$$. the amplitudes and frequencies of component SHMs are

A
$$amplitude 30/4, 10/4; frequencies 3/2,1/2$$

B
$$amplitude 30/4 , 10/4; frequencies 1/2 , 3/2$$

C
$$amplitude 10 , 10 ; frequencies 1/2 , 1/2$$

D
$$amplitude 30/4 ,10 ; frequencies 3/2,2$$

Solution

Given $$x=10{ sin }^{ 3 }(\pi t)$$
It is in the form $$x=\quad A{ sin }^{ 3 }(\omega t)$$
where A= Amplitude. Here, A=10
We know that $$w=2\pi f$$
Here $$\\ 2\pi f=\quad \pi \\ f=\dfrac { 1 }{ 2 } $$
Question 8
1 / -0

A wave of frequency $$100$$ Hz is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of $$10$$ cm from the fixed end of the string. The speeds of incident(and reflected) waves are?

A
$$5$$ $$cms^{-1}$$

B
$$10$$ $$cms^{-1}$$

C
$$20$$ $$cms^{-1}$$

D
$$40$$ $$cms^{-1}$$

Solution

Given frequency $$\nu$$=100 H.
Also distance between two successive nodes$$=>\dfrac { \lambda }{ 2 } =10\\ \lambda =20\quad cm$$
And we know $$\nu =n\lambda \\ n=\frac { \nu }{ \lambda } =\dfrac { 100 }{ 20 } =5\quad cm/s$$
Question 9
1 / -0

Two periodic waves of amplitudes $$A_{1}$$ and $$A_{2}$$ pass through a region. If $$A_{1} > A_{2}$$, the difference in the maximum and minimum resultant amplitude possible is

A
$$2A_{1}$$

B
$$2A_{2}$$

C
$$A_{1}+A_{2}$$

D
$$A_{1}-A_{2}$$.

Solution
Question 10
1 / -0

The maximum particle velocity is $$8$$ times the wave velocity of a progressive wave. If the amplitude of the particle is $$"a"$$. The phase difference between the two particles seperated by a distance of $$""x"$$ is

A
$$\frac{x}{a}$$

B
$$\frac{{8x}}{a}$$

C
$$\frac{{3a}}{x}$$

D
$$\frac{{3\pi x}}{a}$$

Solution