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The equation of a standing wave on a string is $y (x, t) = 0.06 \sin (\frac{2 πx}{3}) \cos (120 πt)$ . The amplitude of a point $0.375 m$ away from the end $x = 0$ is

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Important Questions on Waves

MEDIUM

Physics>Oscillations and Waves>Waves>Standing Waves

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>Oscillations and Waves>Waves>Standing Waves

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>Oscillations and Waves>Waves>Standing Waves

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.

EASY

Physics>Oscillations and Waves>Waves>Standing Waves

The fundamental frequency of a closed organ pipe of length

20 cm

is equal to the second overtone of an organ pipe open at both the ends. The length of the organ pipe open at both the ends is

HARD

Physics>Oscillations and Waves>Waves>Standing 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)

EASY

Physics>Oscillations and Waves>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:

HARD

Physics>Oscillations and Waves>Waves>Standing Waves

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

EASY

Physics>Oscillations and Waves>Waves>Standing Waves

A stretched string fixed at both ends has

m

nodes, then the length of the string will be

EASY

Physics>Oscillations and Waves>Waves>Standing Waves

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>Oscillations and Waves>Waves>Standing Waves

A standing wave pattern can be represented by an equation like

EASY

Physics>Oscillations and Waves>Waves>Standing Waves

The fundamental frequency of an air column in a pipe closed at one end is

100 Hz

. If the same pipe is open at both the ends, the frequencies produced in

Hz

are

HARD

Physics>Oscillations and Waves>Waves>Standing Waves

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

EASY

Physics>Oscillations and Waves>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

HARD

Physics>Oscillations and Waves>Waves>Standing Waves

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>Oscillations and Waves>Waves>Standing Waves

The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?

EASY

Physics>Oscillations and Waves>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

EASY

Physics>Oscillations and Waves>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

EASY

Physics>Oscillations and Waves>Waves>Standing Waves

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>Oscillations and Waves>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)

MEDIUM

Physics>Oscillations and Waves>Waves>Standing Waves

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

The equation of a standing wave on a string is y(x,t)=0.06sin2πx3cos120πt. The amplitude of a point 0.375 m away from the end x=0 is

Important Questions on Waves

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The equation of a standing wave on a string is $y (x, t) = 0.06 \sin (\frac{2 πx}{3}) \cos (120 πt)$ . The amplitude of a point $0.375 m$ away from the end $x = 0$ is