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

EASY

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A person has a hearing range from $20 Hz$ to $20 kHz$ . What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344 m s^{- 1}$ .

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Important Questions on Waves

MEDIUM

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

When a particle of mass

m

is attached to a vertical spring of spring constant

k

and released, its motion, is described by

y (t) = y_{0} \sin^{2} ωt

, where '

y

' is measured from the lower end of upstretched spring. Then

ω

is :

HARD

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = a \hat{i}

and

\vec{B} = a (\cos ω t \hat{i} + \sin ω t \hat{j})

, where a is a constant and

ω = \frac{π}{6} rad s^{- 1} .

|\vec{A} + \vec{B}| = \sqrt{3} |\vec{A} - \vec{B}|

at time

t = τ

for the first time, the value of

τ

in seconds, is_______

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

A uniform thin rope of length

12 m

and mass

6 kg

hangs vertically from a rigid support and a block of mass

2 kg

is attached to its free end. A transverse short wave train of wavelength

6 cm

is produced at the lower and the rope. What is the wavelength of the wave train (in

cm

) when it reaches the top of the rope?

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

An observer on the sea shore observes

54

waves reaching the coast per minute. If the wavelength is

10 m

, the velocity of the wave is

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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?

MEDIUM

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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>Oscillations and Waves>Waves>Speed of a Travelling Wave

A wave is represented by the equation

y = (0.02 m) \sin (5 π x - 20 t) .

The minimum distance between the two particles always having the same speed is. (Assume

x

and

t

are in SI units)

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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

MEDIUM

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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?

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

Which of the following equations represents a travelling wave?

MEDIUM

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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,

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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?

MEDIUM

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is

5 m

, while the distance between one crest and one trough is

1.5 m

. The possible wavelengths (in

m

) of the waves are:

MEDIUM

Physics>Oscillations and Waves>Waves>Speed of a Travelling 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>Oscillations and Waves>Waves>Speed of a Travelling Wave

The equation of a wave is given by

y = 10 \sin ((\frac{2 π}{45}) t + α) .

If the displacement at

t = 0 s

5 cm,

then the total phase at

t = 7.5 s

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

The propagation constant or angular wave number is

EASY

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

A uniform string of length $20 m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is

(Take, $g = 10 m s^{- 2}$ )

HARD

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

A particle performing S.H.M. starts from the equilibrium position and its time period is

16 s

. After

2 s

its velocity is

π m s^{- 1} .

Amplitude of oscillation is

(\cos 45^{o} = \frac{1}{\sqrt 2})

MEDIUM

Physics>Oscillations and Waves>Waves>Speed of a Travelling Wave

A simple harmonic motion is represented by:

y = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t) cm

The amplitude and time period of the motion are:

A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as 344 m s-1.

Important Questions on Waves

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A person has a hearing range from $20 Hz$ to $20 kHz$ . What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344 m s^{- 1}$ .