The electric field of a plane electromagnetic wave is given by E → = E 0 x ^ + y ^ sin k z - ω t . Its magnetic field will be given by

E 0 c - x ^ + y ^ sin k z - ω t

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For a certain transverse standing wave on a long string, an antinode is formed at $x = 0$ and next to it, a node is formed at $x = 0.10 m$ . The position $y (t)$ of the string particle at $x = 0$ is shown in figure.

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Important Questions on Sound Waves

EASY

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

A standing wave can be produced by combining

HARD

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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>Sound Waves>Formation of Standing Waves in an Air Column

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>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is

300 m / s,

the frequency difference between the fundamental and second harmonic of this pipe is __________ Hz.

EASY

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

An electron is constrained to move along the

y

-axis with a speed of

0.1 c

(c is the speed of light) in the presence of electromagnetic wave, whose electric field is

\vec{E} = 30 \hat{j} \sin (1.5 \times 10^{7} t - 5 \times 10^{- 2} x) V m^{- 1} .

where

t

is in seconds and

x

is in meters. The maximum magnetic force experienced by the electron will be: (given

c = 3 \times 10^{8} m s^{- 1}

and electron charge

= 1.6 \times 10^{- 19} C

MEDIUM

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

A stretched string fixed at both ends has

m

nodes, then the length of the string will be

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Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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

HARD

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

Explain the formation of stationary waves by the analytical method. Show that nodes and antinodes are equally spaced in stationary waves.

MEDIUM

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

The electric field of a plane electromagnetic wave is given by $\vec{E} = E_{0} (\hat{x} + \hat{y}) \sin (k z - ω t)$ . Its magnetic field will be given by

MEDIUM

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

A closed pipe of length $300 cm$ contains some sand. A speaker is connected at one of its ends. The frequency of the speaker at which the sand will arrange itself in $20$ equidistant piles is close to (velocity of sound is $300 m s^{- 1}$ )

Question Image

EASY

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

When a sound wave is reflected from the boundary of a denser medium, the compression of the incident wave is returned as:

MEDIUM

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

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?

EASY

Physics>Oscillations and Waves>Sound Waves>Formation of Standing Waves in an Air Column

In sonometer experiment, the string of length

L

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

For a certain transverse standing wave on a long string, an antinode is formed at x=0 and next to it, a node is formed at x=0.10 m. The position y(t) of the string particle at x=0 is shown in figure.

Important Questions on Sound Waves

Learn and Prepare for any exam you want !

For a certain transverse standing wave on a long string, an antinode is formed at $x = 0$ and next to it, a node is formed at $x = 0.10 m$ . The position $y (t)$ of the string particle at $x = 0$ is shown in figure.