Waves Test

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Waves Test - 34

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Weekly Quiz Competition

Question 1
1 / -0

A broadcasting station transmits waves of frequency $$71 \times 10^4 Hz$$ with a speed of $$3 \times 10^8 m/s$$. The wavelength of the wave is :

A
$$418.8m$$

B
$$324.6m$$

C
$$208.4m$$

D
$$422.5m$$

Solution

We have, $$v=n\lambda$$ ,
where $$v=$$ speed of the wave ,
$$n=$$ frequency of the wave ,
$$\lambda=$$ wavelength of the wave ,
given $$n=71\times10^{4}Hz , v=3\times10^{8}m/s$$ ,
therefore , $$\lambda=v/n=\dfrac{3\times10^{8}}{71\times10^{4}}=422.5m$$
Question 2
1 / -0

A certain transverse sinusoidal wave of wavelength $$20\ cm$$ is moving in the positive $$x-$$ direction. The transverse velocity of the particle at $$x = 0$$ as a function of time is shown. The amplitude of the motion is

A
$$\displaystyle \frac{5}{\pi }cm $$

B
$$\displaystyle \frac{\pi}{2 }cm $$

C
$$\displaystyle \frac{10}{\pi }cm $$

D
$$\displaystyle 2\pi\ cm$$

Solution

$$\lambda =20cm,\quad T=4s$$
From the figure
$${ V }_{ max }=5cm/s=A\omega \\ A=\frac { 5 }{ \omega } \\ A=\frac { 5 }{ { 2\pi }/{ T } } =\frac { 5\times 4 }{ 2\pi } \\ \left[ A=\frac { 10 }{ \pi } cm \right] $$
Hence option (C) is correct.
Question 3
1 / -0

An open pipe of length $$33$$cm resonates with frequency of $$1000Hz$$. If the speed of sound is $$330ms^{-1}$$, then this frequency is

A
The fundamental frequency of the pipe

B
The first harmonic of the pipe

C
The second harmonic of the pipe

D
The forth harmonic of the pipe

Solution

Fundamental frequency (first harmonic frequency) of an open organ pipe is given by ,
$$n_{1}=v/\lambda=v/2l$$ ,
where $$v=$$speed of sound in air ($$=330m/s , given$$),
$$\lambda=$$ wavelength ,
$$l=$$ length of organ pipe ($$=33cm=0.33m$$ , given) ,
therefore , $$n_{1}=330/(2\times0.33)=500Hz$$ ,
as an open pipe produces even and odd harmonics , and given frequency is 1000Hz , it is 2 times of the first harmonic frequency , therefore it is second harmonic frequency of the pipe .
Question 4
1 / -0

A particle of mass $$0\cdot 50\ kg$$ executes a simple harmonic motion under a force $$F = -(50\ N/m)x$$. If it crosses the centre of oscillation with a speed of $$10\ m/s$$, then the amplitude of the motion is

A
$$1\ m$$

B
$$2\ m$$

C
$$3\ m$$

D
$$4\ m$$

Solution

A particle executing S.H.M acted upon by a force
F = -(50N/m)$$x$$
it mess m= 0.5kg
so, a = F/m = acceleration
$$\Rightarrow a = -100 x$$
$$\Rightarrow a+{\omega}^{2} x = 0$$
$$\omega$$ = angular frequency $$=\sqrt { 100 } =10 rad/s$$
velocity at mean position
$$\omega A = 10/s$$ A = amplitude of oscillation
$$\Rightarrow A = \dfrac{10}{10} = 1m$$
Question 5
1 / -0

A broadcasting station transmits waves of frequency $$71\times 10^4Hz$$ with speed of $$3\times 10^8m/s$$. The wavelength of the wave is :

A
418.8 m

B
324.6 m

C
208.4 m

D
422.5 m

Solution

We have, $$v=n\lambda$$ ,
where $$v=$$ speed of the wave ,
$$n=$$ frequency of the wave ,
$$\lambda=$$ wavelength of the wave ,
given $$n=71\times10^{4}Hz , v=3\times10^{8}m/s$$ ,
therefore , $$\lambda=v/n=\dfrac{3\times10^{8}}{71\times10^{4}}=422.5m$$
Question 6
1 / -0

Two wave pulses travel in opposite directions on a string and approach each other. The shape of the one pulse is the invert with respect to the other, then

A
the pulses will collide with each other and vanish after collision

B
the pulses will reflect from each other i.e. the pulse going towards right will finally move towards left and vice versa

C
the pulses will pass through each other but their shapes will be modified

D
the pulses will pass through each other without any change in their shape

Solution

As the two wave pulses approach each other on the same string, they do not affect the shape of one another and will pass as they are invert of each other.

when the wave pulses overlap the wave function is the sum of individual wave functions. AT the point where two waves pulses meet, net displacement will be zero.

Option $$D$$ is correct.
Question 7
1 / -0

Speed of sound in air is $$350ms^{-1}$$, fundamental frequency of an open organ pipe of $$50$$cm length will be

A
$$175Hz$$

B
$$350Hz$$

C
$$700Hz$$

D
$$500Hz$$

Solution

Fundamental frequency of an open organ pipe is given by ,
$$n_{1}=v/\lambda=v/2l$$ ,
where $$v=$$speed of sound in air ($$=350m/s , given$$),
$$\lambda=$$ wavelength ,
$$l=$$ length of organ pipe ($$=50cm=0.50m$$ , given) ,
therefore , $$n_{1}=350/(2\times0.50)=350Hz$$
Question 8
1 / -0

The amplitude of an oscillating simple pendulum is 10 cm and its time period is 4 s. Its speed after 1 s when it passes through its equilibrium position is:

A
zero

B
2.0 m/s

C
0.3 m/s

D
0.4 m/s

Solution

In case of SHM, when motion is considered from the equilibrium position, displacement is, y = a sin $$\omega$$t.

So velocity, $$\displaystyle v = \dfrac{dy}{dt} = a\omega cos \omega t$$

$$= a \displaystyle \left ( \frac{2 \pi}{T} \right ) cos \left ( \frac{2 \pi}{T} \right ) t$$

$$= 0.1 \displaystyle \left ( \frac{2 \pi}{4} \right ) cos \left ( \frac{2 \pi}{4} \right ) \times 1 = 0.05 cos \frac{\pi}{2} = 0$$
Question 9
1 / -0

Unit of frequency is........................

A
$$\displaystyle Cycle/\sec ^{2}$$

B
$$\displaystyle Cycle/\sec ^{3}$$

C
$$\displaystyle Cycle/\sec ^{4}$$

D
Hertz

Solution
Question 10
1 / -0

Energy is not propagated by

A
stationary waves

B
electromagnetic waves

C
longitudinal progressive waves

D
transverse progressive Waves

Solution

standing wave patterns are produced as the result of the repeated interference of two waves of identical frequency while moving in opposite directions along the same medium. so in standing waves particles are stationary so propogation of energy cannot take place.
so answer is A.

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Waves Test - 34

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Waves Test - 34

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Question 1

$$418.8m$$

$$324.6m$$

$$208.4m$$

$$422.5m$$

Solution

Question 2

$$\displaystyle \frac{5}{\pi }cm $$

$$\displaystyle \frac{\pi}{2 }cm $$

$$\displaystyle \frac{10}{\pi }cm $$

$$\displaystyle 2\pi\ cm$$

Solution

Question 3

The fundamental frequency of the pipe

The first harmonic of the pipe

The second harmonic of the pipe

The forth harmonic of the pipe

Solution

Question 4

$$1\ m$$

$$2\ m$$

$$3\ m$$

$$4\ m$$

Solution

Question 5

418.8 m

324.6 m

208.4 m

422.5 m

Solution

Question 6

the pulses will collide with each other and vanish after collision

the pulses will reflect from each other i.e. the pulse going towards right will finally move towards left and vice versa

the pulses will pass through each other but their shapes will be modified

the pulses will pass through each other without any change in their shape

Solution

Question 7

$$175Hz$$

$$350Hz$$

$$700Hz$$

$$500Hz$$

Solution

Question 8

zero

2.0 m/s

0.3 m/s

0.4 m/s

Solution

Question 9

$$\displaystyle Cycle/\sec ^{2}$$

$$\displaystyle Cycle/\sec ^{3}$$

$$\displaystyle Cycle/\sec ^{4}$$

Hertz

Solution

Question 10

stationary waves

electromagnetic waves

longitudinal progressive waves

transverse progressive Waves

Solution

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