Waves

01Medium85×since 2002Q8553

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is :

01Medium85×since 2002Q8553

02Easy85×since 2002Q8508

In the wave equation

y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m}

the velocity of the wave will be:

03Easy85×since 2002Q8509

A steel wire with mass per unit length

7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}

is under tension of

70 \mathrm{~N}

. The speed of transverse waves in the wire will be:

04Easy85×since 2002Q8510

A travelling wave is described by the equation

y(x,t) = [0.05\sin (8x - 4t)]

m The velocity of the wave is : [all the quantities are in SI unit]

05Easy85×since 2002Q8472

Tube

A

has bolt ends open while tube

B

has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube

A

and

B

06Easy85×since 2002Q8473

length of a string tied to two rigid supports is

40

cm

. Maximum length (wavelength in

cm

) of a stationary wave produced on it is

07Easy85×since 2002Q8474

When temperature increases, the frequency of a tuning fork

08Easy85×since 2002Q8475

The displacement

y

of a wave travelling in the

x

-direction is given by

$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres

$ where

x

is expressed in metres and

t

in seconds. The speed of the wave - motion, in

m{s^{ - 1}}

, is

09Easy85×since 2002Q8476

The displacement

y

of a particle in a medium can be expressed as,

y = {10^{ - 6}}\,\sin

\left( {100t + 20x + {\pi \over 4}} \right)

m

where

t

is in second and

x

in meter. The speed of the wave is

10Medium85×since 2002Q8477

A sound absorber attenuates the sound level by

20

dB

. The intensity decreases by a factor of

11Medium85×since 2002Q8478

A wave travelling along the

x

-axis is described by the equation

y(x, t)=0.005

\cos \,\left( {\alpha \,x - \beta t} \right).

If the wavelength and the time period of the wave are

0.08

m

and

2.0s

, respectively, then

\alpha

and

\beta

in appropriate units are

12Medium85×since 2002Q8479

The equation of a wave on a string of linear mass density

0.04\,\,kg\,{m^{ - 1}}

is given by

$y = 0.02\left( m \right)\,\sin \left[ {2\pi \left( {{t \over {0.04\left( s \right)}} - {x \over {0.50\left( m \right)}}} \right)} \right].

$ The tension in the string is

13Medium85×since 2002Q8480

The transverse displacement

y(x, t)

of a wave on a string is given by

y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt} \right)}}.

This represents

a:

14Medium85×since 2002Q8481

A cylindrical tube, open at both ends, has a fundamental frequency,

f,

in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :

15Medium85×since 2002Q8482

A sonometer wire of length

1.5

m

is made of steel. The tension in it produces an elastic strain of

1\%

. What is the fundamental frequency of steel if density and elasticity of steel are

7.7 \times {10^3}\,kg/{m^3}

and

2.2 \times {10^{11}}\,N/{m^2}

respectively ?

16Medium85×since 2002Q8483

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 supports is : (take

{\,\,g = 10m{s^{ - 2}}}

)

17Medium85×since 2002Q8484

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r₁ and r₂ . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10^−4 s, the difference in radii,

\left| {} \right.

r₁

-

r₂

\left| {} \right.

is best given by :

18Medium85×since 2002Q8485

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

\left( {{{5\pi } \over 4}x} \right)\,

cos(200

\pi

t). What is the speed of the travelling wave moving in the positive x direction ? (x and t are in meter and second, respectively.)

19Easy85×since 2002Q8486

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :

20Medium85×since 2002Q8487

5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :

Questions per year

85 questions in the bank

Waves

Questions per year

85 questions in the bank