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A string of mass $m$ is fixed at both its ends. The fundamental mode of string is excited and it has an angular frequency $ω$ and the maximum displacement amplitude $A$ . Then:

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Important Questions on Mechanical Wave

HARD

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

The total length of a sonometer wire fixed between two bridges is

110 cm

. Now, two more bridges are placed to divide the length of the wire in the ratio

6 : 3 : 2

. If the tension in the wire is

400 N

and the mass per unit length of the wire is

0.01 kg m^{- 1}

, then the minimum common frequency with which all the three parts can vibrate, is

HARD

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A particle performing S.H.M. starts from the equilibrium position and its time period is

16 s

. After

2 s

its velocity is

π m s^{- 1} .

Amplitude of oscillation is

(\cos 45^{o} = \frac{1}{\sqrt 2})

EASY

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by,

y (x, t) = 0.5 \sin (\frac{5 π}{4} x) \cos (200 π t)

. What is the speed of the travelling wave moving in the positive

x

direction? (

x

and

t

are in meter and second, respectively)

HARD

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the string is

100 m s^{- 1}

. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

MEDIUM

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A simple harmonic motion is represented by:

y = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t) cm

The amplitude and time period of the motion are:

EASY

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A uniform string of length $20 m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is

(Take, $g = 10 m s^{- 2}$ )

MEDIUM

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

Two wires

W_{1}

and

W_{2}

have the same radius

r

and respective, densities

ρ_{1}

and

ρ_{2}

, such that

ρ_{2} = 4 ρ_{1}

. They are joined together at the point

O

, as shown in the figure. The combination is used as a sonometer wire and kept under tension

T

. The point

O

is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in

W_{1}

W_{2}

MEDIUM

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A small speaker delivers

2 W

of audio output. At what distance from the speaker will one detect

120 d B

intensity sound? [Given reference intensity of sound as

10^{- 12} W / m^{2}

]

HARD

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = a \hat{i}

and

\vec{B} = a (\cos ω t \hat{i} + \sin ω t \hat{j})

, where a is a constant and

ω = \frac{π}{6} rad s^{- 1} .

|\vec{A} + \vec{B}| = \sqrt{3} |\vec{A} - \vec{B}|

at time

t = τ

for the first time, the value of

τ

in seconds, is_______

EASY

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencier between these two. The lowest resonant frequency for this string is:

HARD

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A block

M

hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength

λ_{0}

is produced at point O on the rope. The pulse takes time

T_{O A}

to reach point A. If the wave pulse of wavelength

λ_{0}

is produced at point A (Pulse 2) without disturbing the position of M it takes time

T_{O A}

to reach point O. Which of the following options is/are correct?
Question Image

EASY

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

Two waves of amplitudes

A_{1}

and

A_{2}

respectively are superimposed. The ratio between the maximum and minimum intensities of the resultant waves is

9 : 4

. The value of

\frac{A_{2}}{A_{1}}

is [Assume

A_{1} > A_{2}

]

MEDIUM

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A wire of length

2 L,

is made by joining two wires

A

and

B

of same length but different radii

r

and

2 r

and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire

A

p

and that in

B

q

then ratio

p : q

is:

MEDIUM

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A granite rod of

60 cm

length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is

2.7 \times 10^{3} kg m^{- 3}

and its Young's modulus is

9.27 \times 10^{10} Pa

. What will be the fundamental frequency of the longitudinal vibrations?

MEDIUM

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A string is clamped at both the ends and it is vibrating in its

4^{t h}

harmonic. The equation of the stationary wave is

y = 0.3 \sin (0.157 x) c o s (200 π t)

. The length of the string is
(All quantities are in

S I

units.)

MEDIUM

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

n_{1}, n_{2}

and

n_{3}

are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency

n

of the string is given by:

EASY

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A progressive wave travelling along the positive

x -

direction is represented by

y (x, t) = A s i n (k x - ω t + ϕ)

. Its snapshot at

t = 0

is given in the figure.
Question Image

For this wave, the phase

ϕ

is:

EASY

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

In sonometer experiment, the string of length

L

under tension vibrates in second overtone between two bridges. The amplitude of vibration is maximum at

EASY

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

A travelling harmonic wave is represented by the equation

y (x, t) = 10^{- 3} \sin (50 t + 2 x),

where

x

and

y

are in meter and

t

is in seconds. Which of the following is a correct statement about the wave?

HARD

Physics>Mechanics>Mechanical Wave>Progressive and Stationary Waves

The clocktower ("ghantaghar") of Dehradun is famous for the sound of its bell, which can be heard, albeit faintly, upto the outskirts of the city

8 km

away. Let the intensity of this faint sound be

30 dB .

The clock is situated

80 m

high. The intensity at the base of the tower is:-

A string of mass m is fixed at both its ends. The fundamental mode of string is excited and it has an angular frequency ω and the maximum displacement amplitude A. Then:

Important Questions on Mechanical Wave

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A string of mass $m$ is fixed at both its ends. The fundamental mode of string is excited and it has an angular frequency $ω$ and the maximum displacement amplitude $A$ . Then: