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Waves

Multiple Choice Questions

21.

A wave of frequency 500 Hz travels with a speed of 360 ms^-1. The distance between two nearest points which are 60° out of phase is

12 cm
18 cm
50 cm
24 cm

22.

The apparent frequency observed by a moving observer away from a stationary source is 20% less than the actual frequency. If the velocity of sound in air is 330 ms^-1, then the velocity of the observer is

660 ms^-1
330 ms^-1
66 ms^-1
33 ms^-1

23.

A string under tension of 129.6 N produces 10 beats/second, when it vibrates along with a tuning fork. When the tension in the string is increased to 160 N, it vibtrates in unison with the tuning fork. Then, frequency of the tuning fork is

100 Hz
110 Hz
90 Hz
220 Hz

24.

The ionospheric layer acts as a reflector for the frequency range

1 kHz to 10 kHz
3 to 30 MHz
3 to 30 kHz
100 kHz to 1 MHz

25.
Two travelling waves, y₁ = A sin [k(x + ct)] and y₂ = A sin [k(x- ct)] are superposed on a string. The distance between adjacent antinodes is

$\frac{ct}{π}$

$\frac{ct}{2 π}$

$\frac{π}{k}$

$\frac{k}{π}$

$\frac{π}{k}$

Given,

y₁ = A sin [k(x + ct)] ......... (i)

and y₂ = A sin [k(x − ct)] ......... (ii)

By the principle of superposition, the resultant displacement of the particle is given by

y = y₁ + y₂

y = A [sin {k(x + ct)} + sin {k(x − ct)}]

By the formula

$\sin C + \sin D = 2 \sin \frac{C + D}{2} . \cos \frac{C - D}{2}$

We have,

$y = 2 A \sin \frac{kx + kct + kx - kct}{2} . \cos \frac{kx + kct - kx + kct}{2} y = 2 A \sin kx . \cos kct$

For first antinode,

$\sin {kx}_{1} = 1 \sin {kx}_{1} = \sin \frac{π}{2} {kx}_{1} = \frac{π}{2} . . . . . . . (iii)$

For second antinode,

$\sin {kx}_{2} = - 1 \sin {kx}_{2} = \sin \frac{3 π}{2} {kx}_{2} = \frac{3 π}{2} . . . . . . . . (iv)$

∴ The distance between adjacent antinodes

${kx}_{2} - {kx}_{1} = \frac{3 π}{2} - \frac{π}{2} k (x_{2} - x_{1}) = π ∆ x = \frac{π}{k}$

26.

If a stretched wire is vibrating in the second overtone, then the number of nodes and antinodes between the ends of the string are respectively

2 and 2
1 and 2
3 and 4
2 and 3

27.

Pick out the correct statement in the following with reference to stationary wave pattern

In a tube closed at one end, all the harmonics are present
In a tube open at one end, only even harmonics are present
The distance between successive nodes is equal to the wavelength
In a stretched string, the first overtone is the same as the second harmonic

28.

The bulk modulus of a liquid of density 8000 kgm^-3 is 2 x 10⁹ Nm^-2. The speed of sound in that liquid is (in ms^-1)

29.

The vibrations of a string of length 60 cm fixed at both the ends are represented by the equation $y = 2 \sin (\frac{4 πx}{15}) \cos (96 πt)$ , where x and y are in cm. The maximum number of loops that can be formed in it, is