Waves Test

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Waves Test - 81

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Weekly Quiz Competition

Question 1
1 / -0

A wave of frequency 400 Hz has a velocity of 320 $$ms^{-1}$$. The distance between the particles differing in phase by $$90^o$$ is

A
20 cm

B
40 cm

C
60 cm

D
30 cm

Solution
Question 2
1 / -0

Which of the following equations does not represent a progressive wave ?

A
$$y=Asin[\omega (t-\frac { x }{ v } )]$$

B
$$y=Asin[ \frac { 2pi }{ \lambda }(vt-x)] $$

C
$$y=Asin[2\pi (\frac {t}{T}-\frac { x }{ \lambda } )]$$

D
$$y=Asin[2\pi (\frac {t}{T}-\frac { x }{ v } )]$$
Question 3
1 / -0

The spherical waves are emitted in a medium by a source of 5 watt. Assuming that medium does not absorbed energy,the intensity of wave at a distance of 5m from source will be

A
$$ 1 Watt / m^2 $$

B
$$ 1 / (20 \pi ) Watt / m^2 $$

C
$$ 1 / (4 / \pi) watt / m^2 $$

D
$$ 1/5 watt / m^2 $$

Solution
Question 4
1 / -0

Sinusoidal wave having frequency $$500Hz$$ and speed $$800m/s$$.If two point in the medium are separated by distance z having phase difference $$\frac{\pi }{6},$$ then x is

A
$$\frac{2}{{15}}m$$

B
$$\frac{1}{{15}}m$$

C
$$\frac{7}{{15}}m$$

D
$$\frac{8}{{15}}m$$

Solution
Question 5
1 / -0

Consider a wave with frequency $$300\mathrm { Hz }$$ and speed $$350\mathrm { ms } ^ { - 1 } .$$ How far apart are two points $$60 ^ { \circ }$$ out of phase?

A
$$\dfrac { 1 } { 7 } m$$

B
$$\dfrac { 36 } { 7 } \mathrm { m }$$

C
$$\dfrac { 7 } { 36 } \mathrm m$$

D
$$7 \mathrm { m }$$

Solution
Question 6
1 / -0

The energy in the superposition of waves:

A
Is lost

B
Increase

C
remain same, only redistribution occurs

D
None of the above
Question 7
1 / -0

The displacement $$y$$ of a particle, if given by $$y=4\cos^2\left(\dfrac{t}{2}\right)\sin(1000t)$$. This expression may be considered to be a result of the superposition of how many simple harmonic motions?

A
$$4$$

B
$$3$$

C
$$2$$

D
$$5$$

E
$$6$$

Solution

$$\because$$ Equation of displacement of particle is
$$y=4\cos^2(\dfrac{t}{2})\sin (1000t)$$...........(i)

Or $$y=4[\left(\dfrac{1+\cos t}{2}\right)\sin1000t]$$

$$(\because \cos^2x=\dfrac{1+\cos 2x}{2})$$

Or $$y=3\sin 1000t+2\cos t\sin 1000 t$$
Or $$y=2\sin 1000t+\sin 1001t+\sin t 999t$$
$$[2\sin A\cos B=\sin (A+B)+\sin (A-B)]$$
Hence, equation $$(i)$$ is the result of the superposition of three simple harmonic motion.
So, the correct option will be $$(B)$$
Question 8
1 / -0

Source $$S$$ emits microwaves with a constant amplitude. The microwave hit a metal screen $$P$$ and are reflected. A stationary wave is formed between $$S$$ and $$P$$. The wavelength of the microwaves is much smaller than the distance between $$S$$ and$$P$$
A detector $$Q$$ is moved at a slow, constant speed from $$S$$ to $$P$$
What happens to the amplitude of the signal detected by $$Q$$>

A
decreases steadily

B
increases and decreases steadily

C
increases steadily

D
remains constant

Solution

Since the stationary wave is formed ,so there will be Nodes and Antinodes.
We are told that the wavelength of microwave is much smaller than the distance between the S and P.
This means that the stationary wave consists of several wavelength and thus many Nodes (N) and Antinodes (A) are present.
That is like
$$N\ A\ N\ A\ N\ A\ N\ .......$$
The amplitude of the signal detected by Q would increases (at Antinodes) and decreases (at Nodes).
Question 9
1 / -0

A traveling wave is represented by the equation $$ y = \frac{1}{10} sin(60 t + 2x) $$, where x and y in meters and t is in second . this represents a wave
(1) of frequency $$ \frac {30}{\pi} Hz $$
(2) of wavelength $$ \pi m $$
(3)of amplitude 10 cm
(4) moving in the positive x direction
pick out the correct statements from the above.

A
1, 2, 4

B
1, 3, 4

C
1, 2, 3

D
all
Question 10
1 / -0

String $$I$$ and $$II$$ identical lengths and linear mass densities but string $$I$$ is under greater tension than string $$II$$. The accompanying figure shows four different situation, $$A$$ to $$D$$ in which standing wave patterns exists on the two strings. In which situation is it possible that strings $$I$$ and $$II$$ are oscillating at the same resonant frequency?

A

B

C

D

Solution

As we know,
$$v\propto \sqrt T$$

and since $$T_1>T_2$$

then $$v_1>v_2$$

and for both string to have same frequency

$$\lambda _1>\lambda _2$$

this is only shown in option C
so, option (C) is correct.