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A string will break apart if it is placed under too much tensile stress. One type of steel has density. $ρ_{steel} = 10^{4} kg m^{- 3}$ and breaking stress $α = 9 \times 10^{8} N m^{- 2}$ . We make a guitar string from $(4 π)$ gram of this type of steel. It should be able to withstand $(900 π) N$ without breaking. What is highest possible fundamental frequency (in $Hz$ ) of standing waves on the string if the entire length of the string vibrates?

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Important Questions on Superposition of Waves

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 fundamental frequency of a wire stretched by

2 kg wt

100 Hz .

The weight required to produce its octave will be

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.

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

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),_______

MEDIUM

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

A spring, fixed at one end, is connected to a steel wire of length

L

. The other end of the steel wire is connected to an AC source providing a sinusoidal signal of fixed frequency

f

. This stretches the spring and produces standing waves. The spring stretched by

18 cm

produces a standing wave with four antinodes in the steel wire. The stretch of the spring which will produce a standing wave of three antinodes is

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)

MEDIUM

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

A string of length

1 m

and mass

2 \times 10^{- 5} kg

is under tension

T

. When the string vibrates, two successive harmonics are found to occur at frequencies

750 Hz

and

1000 Hz

. The value of tension

T

is _____ newton.

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 ?

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)

HARD

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

A wire of length

30 cm

, stretched between rigid supports, has its

n^{th}

and

{(n + 1)}^{th}

harmonics at

400 Hz

and

450 Hz

, respectively. If tension in the string is

2700 N

, its linear mass density is _____

kg m^{- 1}

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

EASY

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

A guitar string of length

90 cm

vibrates with a fundamental frequency of

120 Hz

. The length of the string producing a fundamental of

180 Hz

will be _____

cm

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 _______.

MEDIUM

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

A wire of density

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

is stretched between two clamps

0.5 m

apart. The extension developed in the wire is

3.2 \times 10^{- 4} m

. If

Y = 8 \times 10^{10} N m^{- 2}

, the fundamental frequency of vibration in the wire will be _____

Hz

EASY

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

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:

MEDIUM

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

A closed organ pipe has a fundamental frequency of

1.5 kHz

. The number of overtones that can be distinctly heard by a person with this organ pipe will be

(

Assume that the highest frequency a person can hear is

20,000 Hz

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)

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 :

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

Important Questions on Superposition of Waves

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