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The equation of a wave on a string of linear mass density $0.04 kg m^{- 1}$ is given by, $y = 0.02 (m) \sin [2 π (\frac{t}{0.04 (s)} - \frac{x}{0.50 (m)})]$ .

The tension in the string is $n \times 10^{- 2} N$ . Write the value of $n$ .

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Important Questions on Waves

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A string of length

1 m

and mass

5 g

is fixed at both ends. The tension in the string is

8 .0 N

. The string is set into vibration using an external vibrator of frequency

100 Hz

. The separation between successive nodes on the string is close to

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

HARD

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A block

M

hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength

λ_{0}

is produced at point O on the rope. The pulse takes time

T_{O A}

to reach point A. If the wave pulse of wavelength

λ_{0}

is produced at point A (Pulse 2) without disturbing the position of M it takes time

T_{O A}

to reach point O. Which of the following options is/are correct?
Question Image

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A sound wave travelling in water has wavelength

0.4 m

. Is this wave audible in air? (The speed of sound in water

= 1400 m s^{- 1}

)

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

The mass per unit length of a uniform wire is

0.135 g {cm}^{- 1}

. A transverse wave of the form

y = - 0.21 \sin (x + 30 t)

is produced in it, where

x

is in meter and

t

is in second. Then, the expected value of tension in the wire is

x \times 10^{- 2} N

. Value of

x

is (Round-off to the nearest integer)

EASY

Physics>Mechanical Wave>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

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A heavy ball of mass

M

is suspended from the ceiling of a car by a light string of mass

m (m ≪ M) .

When the car is at rest, the speed of transverse waves in the string is

60 m s^{- 1}

. When the car has acceleration

a

, the wave-speed increases to

60.5 m s^{- 1}

. The value of

a

in terms of gravitational acceleration

g

is closed to:

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

Given below are two different graphs of variation of density (or pressure) of the medium with position in figure

(1)

and with time in figure

(2)

as a wave passes through the medium.
Question Image

What will be the speed of the wave in the given medium?

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by

4 %

, will be ___

%

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

The amplitude of wave disturbance propagating in the positive

x

-direction is given by

y = \frac{1}{(1 + x)^{2}}

at time

t = 0

and

y = \frac{1}{1 + (x - 2)^{2}}

t = 1 s

, where

x

and

y

are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be

m s^{- 1} .

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

When light wave travels from air to glass

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A transverse wave propagating on a stretched string of linear density $3 \times 10^{- 4} {kgm}^{- 1}$ is represented by the equation

$y = 0.2 \sin (1.5 x + 60 t)$

where, $x$ in metres and $t$ is in seconds. The tension in the string (in Newton) is

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

The wavelength of a wave is

3 m

. If the velocity of the wave is

330 {ms}^{- 1}

, then find the frequency of that wave. Calculate the time period if the frequency of that wave is reduced to half of its value.

EASY

Physics>Mechanical Wave>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?

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A steel wire of

0.72 m

long has a mass of

5 \times 10^{- 3} kg

. If the wire is under a tension of

60 N

. What is the speed of transverse waves on the wire?

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

The distance between two successive minima of a transverse wave is

2.7 m

. Five crests of the wave pass a given point along the direction of travel every

15.0 s

. The speed of the wave is

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A person has a hearing range from

20 Hz - 20 KHz

. The typical wavelengths of sound waves in air corresponding to these two frequencies are: (speed of sound in air is

344 m s^{- 1}

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

The speed of sound in an elastic string when it is extended by $x m$ is $v .$ If it is further extended to $3 x m,$ the speed of the sound becomes

EASY

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A steel wire has a length of

90 cm

which is under a constant tension of

100 N .

The speed of the transverse waves that can be produced in the wire will be (take the mass of the steel wire to be

6 \times 10^{- 3} kg

)

MEDIUM

Physics>Mechanical Wave>Waves>Speed of a Travelling Wave

A uniform rope of length

L

and mass

m_{1}

, hangs vertically from a rigid support. A block of mass

m_{2}

is attached to the free end of the rope. A transverse pulse of wavelength

λ_{1}

is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

λ_{2}

. The ratio

\frac{λ_{2}}{λ_{1}}

is:

The equation of a wave on a string of linear mass density 0.04 kg m-1 is given by, y=0.02msin⁡2πt0.04(s)-x0.50(m). The tension in the string is n×10-2 N. Write the value of n.

Important Questions on Waves

Learn and Prepare for any exam you want !

The equation of a wave on a string of linear mass density $0.04 kg m^{- 1}$ is given by, $y = 0.02 (m) \sin [2 π (\frac{t}{0.04 (s)} - \frac{x}{0.50 (m)})]$ .

The tension in the string is $n \times 10^{- 2} N$ . Write the value of $n$ .