Waves Test

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Waves Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

A body is vibrating 7200 times in one minute. If the velocity of sound is 360 m/s, find (i) frequency of the vibration in Hz, (ii) the wavelength of the sound produced.

A
$$120\ Hz, 3\ m$$

B
$$140\ Hz, 3\ m$$

C
$$120\ Hz, 4\ m$$

D
$$140\ Hz, 4\ m$$

Solution

(i) Frequency of vibration is defined as number of vibration per second ,
so , frequency , $$f=$$number of vibrations/time in second $$=7200/60=120Hz$$ ,
(ii) Now given , $$v=360m/s$$ and $$f=120Hz$$
by , $$v=f\lambda$$ ,
or $$\lambda=v/f=360/120=3m$$
Question 2
1 / -0

A .......... is any disturbance that transmits energy without carrying any material with it.

A
Wave

B
Temperature

C
Vibration

D
Echolocation
Question 3
1 / -0

A particle moves on the X-axis is according to the equation $$x = A+B\space \sin\omega t$$. The motion is simple harmonic with amplitude:

A
$$A$$

B
$$B$$

C
$$A+B$$

D
$$\sqrt{A^2 + B^2}$$

Solution

The equation $$y = B sin (wt) + A$$ suggests that the particle is executing Simple Harmonic Motion about $$A$$ which is the mean position and the amplitude of oscillation of the SHM (about $$A$$) is equal to $$B$$.
Question 4
1 / -0

Sound travels with a speed of about 330m/s. What is the wavelength of sound whose frequency is 660 Hz?

A
0.5 m

B
1 m

C
2 m

D
1.5 m

Solution

We have , $$v=f\lambda$$ ,
given $$v=330m/s , f=660Hz$$ ,
therefore , $$\lambda=v/f=330/660=0.5m$$
Question 5
1 / -0

Which of the following parameters of a wave undergoes a change when wave is reflected from a boundary ?

A
$$Intensity$$

B
$$Phase$$

C
$$Speed$$

D
$$Frequency$$

Solution

When the wave undergoes reflection against a rigid body it results into change of shape so as to maintain the boundary condition at the wall i.e. the particle at the boundary remains at rest.
Due to this there is change of phase.
Frequency, wavelength and speed remain constant.
Hence option (B) is correct.
Question 6
1 / -0

In a ripple tank, $$10$$ full ripples/s are produced. The distance between peaks of consecutive trough and crest is $$15 cm$$. Calculate the velocity of the ripples.

A
$$2 m/s$$

B
$$3 m/s$$

C
$$4 m/s$$

D
$$6 m/s$$

Solution

The relationship between frequency, speed of sound and wavelength of a sound wave is given as $$Frequency=\dfrac { Speed\quad of\quad sound\quad (m/s) }{ Wavelength\quad (m) } \quad $$.

In the question, it is given that the frequency is $$10 Hz$$ and the total wavelength (twice the distance between peaks of consecutive trough and crest) is $$2\times 15\quad cm\quad =\quad 30\quad cm\quad =\quad 0.03\quad meters$$.

The speed of the wave can be derived as follows.
$$Speed\quad of\quad wave\quad (v)=\quad Frequency\quad (f)\times \quad Wavelength\quad (\lambda) $$

That is, $$v=f\times \lambda \quad =\quad 10\quad Hz\times 0.030\quad m\quad =\quad 3\quad m/s$$.

Hence, the wavelength of the wave is 3 m/s
Question 7
1 / -0

The maximum displacement of a vibrating body in the medium from its mean position is called _________. Its SI unit is _________.

A
Frequency, Hertz

B
Waves, Decibel

C
Amplitude, Metre

D
Time-period, Second
Question 8
1 / -0

Two SHMs are represented by $$\displaystyle y=a\sin(w t-kx)$$ and $$\displaystyle y=b\cos (w t -kx)$$. The phase difference between the two is

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

B
$$\displaystyle \frac{\pi}{4}$$

C
$$\displaystyle \frac{\pi}{6}$$

D
$$\displaystyle \frac{3\pi}{4}$$
Solution
$$cos\Theta=sin(90-\Theta)$$
$$y=asin(\omega t-kx)$$
$$y=bcos(\omega t-kx)$$ $$=bcos(\frac{\pi}{2}-(\omega t-kx))$$
It is clearly seen that the there is a phase difference of $$\frac{\pi}{2}$$ between the two SHMs
Question 9
1 / -0

When two waves of the same amplitude and frequency but having a phase difference of $$\displaystyle \phi $$ travelling with the same speed in the same direction (positive x) meets at a point then

A
their resultant amplitude will be twice that of a single wave but the frequency will be same

B
their resultant amplitude and frequency will both be twice that of a single wave

C
their resultant amplitude will depend on the phase angle while the frequency will be the same

D
the frequency and amplitude of the resultant wave will depend upon the phase angle

Solution

When the two waves of same amplitude & frequency having phase difference $$\phi $$, meets, travelling in the same direction, their resultant amplitude will depend on the phase difference.
While frequency will remain same.
Hence option (C) is correct.
Question 10
1 / -0

Two particles execute S.H.M of same amplitude and frequency along the same straight line from same mean position. They cross one another without collision, when going in opposite direction, each time their displacement is half of their amplitude. The phase-difference between them is

A
$$\displaystyle 0^{\circ}$$

B
$$\displaystyle 120^{\circ}$$

C
$$\displaystyle 180^{\circ}$$

D
$$\displaystyle 135^{\circ}$$

Solution

Since both particles have same amplitude and frequency, its equation is
$${ x }_{ 1 }={ x }_{ m }\cos { \omega } t\\ { x }_{ 2 }={ x }_{ m }\cos { \left( \omega t+\phi \right) } \\ \\ $$
Crossing happens when $${ x }_{ 1 }=\frac { { x }_{ m } }{ 2 } \\ $$
So $${ x }_{ 1 }={ x }_{ m }\cos { \omega } t\\ \frac { { x }_{ m } }{ 2 } ={ x }_{ m }\cos { \omega } t\\ \omega t=\frac { \pi }{ 3 } $$
Similarly for $${ x }_{ 2 }$$, but it is moving in different direction so the closest value of $$\omega t+\phi =\frac { 2\pi }{ 3 } $$
$$\omega t+\phi =\frac { 2\pi }{ 3 } \\ \frac { \pi }{ 3 } +\phi =\frac { 2\pi }{ 3 } \\ \phi =\frac { \pi }{ 3 } $$
Ans: 120 degreee

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Waves Test - 32

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Waves Test - 32

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Question 1

$$120\ Hz, 3\ m$$

$$140\ Hz, 3\ m$$

$$120\ Hz, 4\ m$$

$$140\ Hz, 4\ m$$

Solution

Question 2

Wave

Temperature

Vibration

Echolocation

Question 3

$$A$$

$$B$$

$$A+B$$

$$\sqrt{A^2 + B^2}$$

Solution

Question 4

0.5 m

1 m

2 m

1.5 m

Solution

Question 5

$$Intensity$$

$$Phase$$

$$Speed$$

$$Frequency$$

Solution

Question 6

$$2 m/s$$

$$3 m/s$$

$$4 m/s$$

$$6 m/s$$

Solution

Question 7

Frequency, Hertz

Waves, Decibel

Amplitude, Metre

Time-period, Second

Question 8

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

$$\displaystyle \frac{\pi}{4}$$

$$\displaystyle \frac{\pi}{6}$$

$$\displaystyle \frac{3\pi}{4}$$

Solution

Question 9

their resultant amplitude will be twice that of a single wave but the frequency will be same

their resultant amplitude and frequency will both be twice that of a single wave

their resultant amplitude will depend on the phase angle while the frequency will be the same

the frequency and amplitude of the resultant wave will depend upon the phase angle

Solution

Question 10

$$\displaystyle 0^{\circ}$$

$$\displaystyle 120^{\circ}$$

$$\displaystyle 180^{\circ}$$

$$\displaystyle 135^{\circ}$$

Solution

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