A wave pulse in a string is described by the equation y 1 = 5 3 x - 4 t 2 + 2 and another wave pulse in the same string is described by y 2 = - 5 3 x + 4 t - 6 2 + 2 . The values of y 1 , y 2 and x are in metres and t is in seconds. Which of the following statement is correct?

At x = 1 m , y 1 and y 2 always cancel

y 1 travels along - x -direction and y 2 along + x -direction

Both y 1 and y 2 travel along + x -direction

At time t = 1 s , y 1 and y 2 exactly cancel everywhere

At time t = 3 s , y 1 and y 2 exactly cancel everywhere

MEDIUM

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The transverse displacement of a wave on string is given by $y (x, t) = e^{- ({ax}^{2} + {bt}^{2} + 2 \sqrt{ab} xt)}$ , this represents a _______

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Important Questions on Sound

MEDIUM

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A transverse wave propagating along $x$ -axis is represented by

$y (x, t) = 8.0 \sin (0.5 π x - 4 π t - \frac{π}{4})$

where $x$ is in meters and $t$ is in seconds. The speed of the wave is

MEDIUM

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

Assume that the displacement

(s)

of air is proportional to the pressure difference

(Δ p)

created by a sound wave. Displacement

(s)

further depends on the speed of sound

(v)

, density of air

(ρ)

and the frequency

(f)

. If

Δ p = 10 Pa, n = 300 m s^{- 1}, p = 1 kg m^{- 3}

and

f = 1000 Hz

, then

s

will be of the order of (take the multiplicative constant to be

1

)

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

In a resonance tube experiment when the tube is filled with water up to a height of

17.0 cm,

from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of

24.5 cm .

If the velocity of sound in air is

330 m s^{- 1},

the tuning fork frequency is :

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A travelling harmonic wave is represented by the equation

y (x, t) = 10^{- 3} \sin (50 t + 2 x),

where

x

and

y

are in meter and

t

is in seconds. Which of the following is a correct statement about the wave?

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

The figure below shows pressure variation in two different sound waves in air with time at a given position. Both the figures are drawn to the same scale.

Question Image

Which of the following statement is true?

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A pendulum vibrates with a time period of

1

second. The sound produced in it is in the range of

MEDIUM

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from

420 Hz

490 Hz

when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is

330 {ms}^{- 1}

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A sound wave of frequency

245 Hz

travels with the speed of

300 {m s}^{- 1}

along the positive x-axis. Each point of the wave moves to and fro through a total distance of

6 cm

. What will be the mathematical expression of this travelling wave?

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A simple wave motion is represented by $y = 5 (\sin 4 π t + \sqrt{3} \cos 4 π t)$ . Its amplitude is

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A progressive wave travelling along the positive

x -

direction is represented by

y (x, t) = A s i n (k x - ω t + ϕ)

. Its snapshot at

t = 0

is given in the figure.
Question Image

For this wave, the phase

ϕ

is:

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A bomb blasts on moon. Its sound will be heard on earth after

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

The maximum transverse velocity and maximum transverse acceleration of a harmonic wave in a

o n e - d i m e n s i o n a l

string are

1 m s^{- 1}

and

1 m s^{- 2}

respectively. The phase velocity of the wave is

1 m s^{- 1}

. The waveform is

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

On an average, a human heart is found to beat

72

times a minute. Its frequency and period are

HARD

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A ball is moving uniformly in a circular path of radius

1 m

with a time period of

1.5 s

. If the ball is suddenly stopped at

t = 8.3 s,

the magnitude of the displacement of the ball with respect to its position at

t = 0 s

is closest to:

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

Which of the following equations represents a travelling wave?

MEDIUM

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

The transverse displacement at position $x$ and time $t$ in a string due to a travelling wave is given by $y (x, t) =$ $3.0 \cos (π x - 4 π t) cm$ , where $x$ is in centimeters and $t$ is in seconds. Which of the following statements is wrong?

Question Image

EASY

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

To propagate both longitudinal and transverse waves, a material must have

MEDIUM

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A transverse wave travels on a taut steel wire with a velocity of

v

when tension in it is

2.06 \times 10^{4} N .

When the tension is changed to

T,

the velocity changed to

\frac{v}{2} .

The value of

T

is close to:

MEDIUM

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A wave pulse in a string is described by the equation

y_{1} = \frac{5}{{(3 x - 4 t)}^{2} + 2}

and another wave pulse in the same string is described by

y_{2} = \frac{- 5}{{(3 x + 4 t - 6)}^{2} + 2}

. The values of

y_{1}, y_{2}

and

x

are in metres and

t

is in seconds. Which of the following statement is correct?

MEDIUM

Physics>Waves and Oscillations>Sound>Mathematical Expression of a Wave

A transverse wave of frequency

500 Hz

and speed

100 m s^{- 1}

is travelling in the positive,

x

direction on a long string. A time

t = 0 s

the displacements at

x = 0.0 m

and at

x = 0.25 m

are

0.0 m

and

0.02 m,

respectively. The displacement at

x = 0.2 m

t = 5 \times 10^{4} s

is,

The transverse displacement of a wave on string is given by yx, t=e-ax2+bt2+2ab xt, this represents a _______

Important Questions on Sound

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The transverse displacement of a wave on string is given by $y (x, t) = e^{- ({ax}^{2} + {bt}^{2} + 2 \sqrt{ab} xt)}$ , this represents a _______