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A uniform string of length L and mass M is fixed at both ends while it is subject to a tension T. It can vibrate at frequencies $(v)$ given by the formula (where $n = 1,2, 3, \dots .$ )

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Important Questions on Waves

MEDIUM

General Science>Physics>Waves>Standing 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:

MEDIUM

General Science>Physics>Waves>Standing 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

General Science>Physics>Waves>Standing 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.)

EASY

General Science>Physics>Waves>Standing Waves

A stretched string fixed at both ends has

m

nodes, then the length of the string will be

HARD

General Science>Physics>Waves>Standing Waves

Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire then the ratio of the lengths of the first wire to second wire is

MEDIUM

General Science>Physics>Waves>Standing Waves

A string

2.0 m

long and fixed at its ends is driven by a

240 H z

vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

MEDIUM

General Science>Physics>Waves>Standing 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

General Science>Physics>Waves>Standing Waves

Answer the following by appropriately matching the lists based on the information given in the paragraph.
A musical instrument is made using four different metal strings,

1, 2, 3

and

4

with mass per unit length

μ, 2 μ, 3 μ

and

4 μ

respectively. The instrument is played by vibrating the strings by varying the free length in between the range

L_{0}

and

2 L_{0} .

It is found that in string-

1 (μ)

at free length

L_{0}

and tension

T_{0}

the fundamental mode frequency is

f_{0} .

List-I gives the above four strings while list-II lists the magnitude of some quantity.

	List I		List II
(I)	String $- 1 (μ)$	(P)	$1$
(II)	String $- 2 (2 μ)$	(Q)	$\frac{1}{2}$
(III)	String $- 3 (3 μ)$	(R)	$\frac{1}{\sqrt{2}}$
(IV)	String $- 4 (4 μ)$	(S)	$\frac{1}{\sqrt{3}}$
		(T)	$\frac{3}{16}$
		(U)	$\frac{1}{16}$

If the tension in each string is

T_{0},

the correct match for the highest fundamental frequency in

f_{0}

units will be,

MEDIUM

General Science>Physics>Waves>Standing 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}

EASY

General Science>Physics>Waves>Standing 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)

EASY

General Science>Physics>Waves>Standing Waves

A stretched wire of length

260 cm

is set into vibrations. It is divided into three segments whose frequencies are in the ratio

2 : 3 : 4

. Their lengths must be

MEDIUM

General Science>Physics>Waves>Standing Waves

A sonometer wire of length

1 .5 m

is made of steel. The tension in it produces an elastic strain of

1%

. What is the fundamental frequency of steel if density and elasticity of steel are

7 .7 \times 10^{3} kg m^{- 3}

and

2 .2 \times 10^{11} N m^{- 2}

respectively?

HARD

General Science>Physics>Waves>Standing Waves

Find the wrong statement form the following about the equation of stationary wave given by

Y = 0.04 \cos (π x) \sin (50 π t)

m where

t

is in second. Then for the stationary wave.

EASY

General Science>Physics>Waves>Standing Waves

A string is vibrating in its fifth overtone between two rigid supports

2.4 m

apart. The distance between successive node and antinode is

MEDIUM

General Science>Physics>Waves>Standing Waves

A wire of length

L

and mass per unit length

6.0 \times 10^{- 3} k g m^{- 1}

is put under tension of

540 N .

Two consecutive frequencies that it resonates at are:

420 H z

and

490 H z .

Then

L

in meters is :

EASY

General Science>Physics>Waves>Standing Waves

The equation of a stationary wave is

y = 2 \sin (\frac{π x}{15}) \cos (48 π t)

. The distance between a node and its next antinode is

HARD

General Science>Physics>Waves>Standing Waves

Answer the following by appropriately matching the lists based on the information given in the paragraph.
A musical instrument is made using four different metal strings,

1, 2, 3

and

4

with mass per unit length

μ, 2 μ, 3 μ

and

4 μ

respectively. The instrument is played by vibrating the strings by varying the free length in between the range

L_{0}

and

2 L_{0} .

It is found that in string-

1 (μ)

at free length

L_{0}

and tension

T_{0}

the fundamental mode frequency is

f_{0} .

List-I gives the above four strings while list-II lists the magnitude of some quantity.

	List I		List II
(I)	String $- 1 (μ)$	(P)	$1$
(II)	String $- 2 (2 μ)$	(Q)	$\frac{1}{2}$
(III)	String $- 3 (3 μ)$	(R)	$\frac{1}{\sqrt{2}}$
(IV)	String $- 4 (4 μ)$	(S)	$\frac{1}{\sqrt{3}}$
		(T)	$\frac{3}{16}$
		(U)	$\frac{1}{16}$

The length of the strings

1, 2, 3

and

4

are kept fixed at

L_{0}, \frac{3 L_{0}}{2}, \frac{5 L_{0}}{4}

and

\frac{7 L_{0}}{4},

respectively. Strings

1, 2, 3

and

4

are vibrated at their

1^{s t}, 3^{r d}, 5^{t h}

and

14^{t h}

harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of

T_{0}

will be.

HARD

General Science>Physics>Waves>Standing 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

EASY

General Science>Physics>Waves>Standing 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

General Science>Physics>Waves>Standing 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:

A uniform string of length L and mass M is fixed at both ends while it is subject to a tension T. It can vibrate at frequencies v given by the formula (where n=1,2,3,…. )

Important Questions on Waves

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A uniform string of length L and mass M is fixed at both ends while it is subject to a tension T. It can vibrate at frequencies $(v)$ given by the formula (where $n = 1,2, 3, \dots .$ )