MEDIUM

Earn 100

Distinguish between overtones and harmonics.

Important Questions on Superposition of Waves

MEDIUM

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

A standing wave is produced on a string fixed at one end and free at other. The length of string must be an _______.

HARD

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

The ratio of the fundamental frequencies of two identical strings after one of them was stretched by

2 %

and the other by

4 %

is (Assume that the tension is proportional to the elongation)

HARD

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

A stretched sonometer wire is in unison with a tuning fork. When the length of the wire is increased by 5%, the number of beats heard per second is 10. Find the frequency of the tuning fork.

MEDIUM

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

Two strings of the same material and same length are given equal tension. If they are vibrating with fundamental frequencies

1600 Hz

and

900 Hz,

then the ratio of their respective diameters is

HARD

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

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)

HARD

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

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

HARD

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

In stationary wave, the distance between a node and its adjacent anti-node is____.

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

The fundamental frequency of a wire stretched by

2 kg wt

100 Hz .

The weight required to produce its octave will be

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

A wire of density

9 \times 10^{- 3} kg {cm}^{- 3}

is stretched between two clamps

1 m

apart. The resulting strain in the wire is

4.9 \times 10^{- 4}

. The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire

Y = 9 \times 10^{10} {Nm}^{- 2}

), (to the nearest integer),_______

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

A standing wave pattern can be represented by an equation like

MEDIUM

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

When a string is divided into three segments of lengths $l_{1}, l_{2} and l_{3}$ the fundamental frequencies of these three segments are $ν_{1}, ν_{2} and ν_{3}$ respectively. The original fundamental frequency $ν$ of the string is

HARD

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

Explain the formation of stationary waves in stretched strings and hence deduce the law of transverse waves in stretched strings.

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

Two identical strings

X

and

Z

made of same material have tension

T_{X}

and

T_{Z}

in then if their fundamental frequencies are

450 Hz

and

300 Hz

, respectively, then the ratio

T_{X} / T_{Z}

is :

HARD

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

In Melde’s experiment, when tension in the string is

10 g

wt then three loops are obtained. Determine the tension in the string required to obtain four loops, if all other conditions are constant.

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

The length of the string of a musical instrument is

90 cm

and has a fundamental frequency of

120 Hz

Where should it be pressed to produce fundamental frequency of

180 Hz ?

MEDIUM

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

A wire having a linear mass density

9.0 \times 10^{- 4} kg m^{- 1}

is stretched between two rigid supports with a tension of

900 N .

The wire resonates at a frequency of

500 Hz .

The next higher frequency at which the same wire resonates is

550 Hz .

The length of the wire is ___________

m .

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

The equation of stationary wave on a string clamped at both ends and vibrating in third harmonic is given by

y = 0.5 \sin (0.314 x) \cos (600 π t),

where

x

and

y

are in

cm

and

t

in second. The length of the vibrating string is

(π = 3.14)

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

Two identical wires are vibrating in unison. If the tension in one of the wires is increased by

2 %

, five beats are produced per second by the two vibrating wires. The initial frequency of each wire is

(\sqrt{1.02} = 1.01)

EASY

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

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)

MEDIUM

Physics>Waves and Oscillations>Superposition of Waves>Formation of Stationary Waves on String

Show that only odd harmonics are present as overtones in the case of an air column vibrating in a pipe closed at one end.

Distinguish between overtones and harmonics.

Important Questions on Superposition of Waves

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