Oscillations and Waves Test

Result

Oscillations and Waves Test - 3

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Question 1
1 / -0

A source and an observer are approaching each other with 50 ms^-1 velocity. What will be the original frequency if the observer receives 400 cycles/s? Take speed of sound = 340 m/s

A
f_o 300 cycles/s

B
f_o 320 cycles/s

C
f_o 340 cycles/s

D
f_o 330 cycles/s

Solution

As the obsererver and source both are approaching each other, so the apparent frequency

Where v is the velocity of the sound, v₀ is the velocity of the observer, v_s is the velocity of the source, f₀ is the actual frequency and f' is the apparent frequency.
v₀ = 50 m/s, v_s = 50 m/s, v = 340 m/s, f' = 400 Hz

cycles per second (Hz)
Question 2
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A ball of mass 2 kg is moving with a velocity of 3 m/s. It collides with a spring of natural length 2 m and force constant 72 N/m. What will be the length of the compressed spring?

A
2 m

B
1.5 m

C
1 m

D
0.5 m

Solution

The kinetic energy of spring-ball system is conserved.
Let spring is compressed by a length x.
Kinetic energy of ball = Potential energy of spring

Hence, length of compressed spring

Thus, the length of the spring after compression is 1.5 m.
Question 3
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A particle in SHM is described by the displacement equation, x(t) = A cos (ωt + θ). If the initial (t = 0) position of the particle is 1 cm and its initial velocity is π cm/s, then what is its amplitude? (The angular frequency of the particle is πs^-1.)

A
1 cm

B
cm

C
2 cm

D
2.5 cm

Solution
Question 4
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The angular amplitude of a simple pendulum is θ₀. What will be the maximum tension in its string?

A
mg(1 - θ₀)

B
mg(1 + θ₀)

C
mg(1 - θ₀²)

D
mg(1 + θ₀²)

Solution
Question 5
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The time period of a particle in simple harmonic motion is 8 seconds. At t = 0, it is at the mean position. The ratio of the distances travelled by it in the 1^st second and the 2^nd second is

A

B

C

D

Solution
Question 6
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A particle is executing two different simple harmonic motions mutually perpendicular to different amplitudes and having a phase difference of π/2. The path of the particle will be

A
circular

B
straight

C
parabolic

D
elliptical

Solution

Let x = a sin (ωt + δ) ...(i)
y = b sin ωt ...(ii)
are two perpendicular SHM waves.
The resultant can be obtained by eliminating ωt from Eqs. (i) and (ii), we get

sin ωt =
∴ cos ωt =
∴ = sin ωt cos δ + cos ωt sin δ

or cos δ + sin δ
⇒
⇒ cosδ = sin²δ
Given, phase difference between the waves is δ = .
So, resultant equation becomes, = 1

This represents the regular ellipse.
Question 7
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A particle executes linear simple harmonic motion with amplitude of 2 cm. When the particle is at 1 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Its time period (in seconds) is

A

B

C

D

Solution
Question 8
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A particle starts SHM from a mean position. Its amplitude is 'a' and total energy is E. At one instant, its kinetic energy is 3E/4. Its displacement at that instant is

A

B

C

D

Solution
Question 9
1 / -0

Two identical springs are connected in series and parallel as shown in the figure. If f_s and f_p are frequencies of series and parallel arrangements, respectively, then what is ?

A
1 : 2

B
2 : 1

C
1 : 3

D
3 : 1

Solution
Question 10
1 / -0

The time period of a simple pendulum of length l is T₁, and the time period of a uniform rod of the same length l pivoted at one end and oscillating in a vertical plane is T₂. The amplitude of oscillations in both the cases is small. Then, T₁/T₂ is

A

B
1

C

D

Solution
Question 11
1 / -0

A simple pendulum with a bob of mass m and a conducting wire of length L swings under gravity through an angle 2θ. The earth's magnetic field component in the direction perpendicular to the swing is B. The maximum potential difference induced across the pendulum is

A
2BL sin(gL)^1/2

B
BL sin(gL)

C
BL sin(gL)^3/2

D
BL sin(gL)²

Solution
Question 12
1 / -0

A simple pendulum is released from A, as shown in the figure. If m and l represent the mass of the bob and the length of the pendulum, respectively, then the gain in kinetic energy at B is

A

B

C
mgl

D
mgl

Solution

Loss of potential energy in coming from A to B = mgh
= mgl cos 30°
= mgl

Kinetic energy gained = loss of potential energy
= mgl
Question 13
1 / -0

The equation of a simple harmonic wave is given by y = 5 sin (100t - x), where x and y are in metres and t is in seconds. The period of the wave will be

A
0.04 s

B
0.01 s

C
1 s

D
5 s

Solution
Question 14
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A uniform wire of linear density 0.004 kg-m^-1 when stretched between two rigid supports, with a tension 3.6 × 10² N, resonates with a frequency of 420 Hz. The next harmonic frequency with which the wire resonates is 490 Hz. The length of the wire in metres is

A
1.41

B
2.14

C
2.41

D
3.14

Solution

∴ n =

or 490 - 420 =
or 70 = × 300

or l = = 2.14 m
Question 15
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The frequency of a tuning fork is 256 Hz. The velocity of sound in air is 344 ms^-1. The distance travelled (in metres) by the sound during the time in which the tuning fork completes 32 vibrations is

A
21 m

B
43 m

C
86 m

D
129 m

Solution
Question 16
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What is the beat frequency produced when the following two waves are sounded together?

x₁ = 10 sin (404πt - 5πx), x₂ = 10 sin (400πt - 5πx)

A
4 Hz

B
1 Hz

C
3 Hz

D
2 Hz

Solution
Question 17
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A point mass m is suspended at the end of a massless wire of length L and cross section A. If Y is Young's modulus for the wire, what will be the frequency of oscillation for the SHM along the vertical line?

A

B

C

D

Solution

n =
and

n =
Question 18
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The factor determining the pitch of a tuning fork is

A
physical condition

B
frequency

C
wavelength

D
None of these

Solution

Pitch is a characteristic of musical sound and depends upon its frequency. The tone of higher frequency is interpreted as shrill and that of low frequency is interpreted as grave.
Question 19
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When both the listener and the source are moving towards each other, then which of the following is true regarding the frequency and wavelength of the wave observed by the observer?

A
More frequency, less wavelength

B
More frequency, more wavelength

C
Less frequency, less wavelength

D
More frequency, constant wavelength

Solution
Question 20
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The first overtone of a stretched wire of given length is 320 Hz. The first harmonic is

A
320 Hz

B
160 Hz

C
480 Hz

D
640 Hz

Solution