1
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $$340\,m{s^{ - 1}}$$)
A
$$220$$ $$cm$$
B
$$190$$ $$cm$$
C
$$180$$ $$cm$$
D
$$200$$ $$cm$$
2
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
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.)
A
160 m/s
B
90 m/s
C
180 m/s
D
120 m/s
3
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
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 :
A
1 cm
B
0.05 cm
C
0.5 cm
D
0.01 cm
4
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Two wires W1 and W2 have the same radius r and respective densities $$\rho$$1 and $$\rho$$2 such that ρ2 = 4$$\rho$$1 . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2 is :

A
1 : 1
B
1 : 2
C
1 : 3
D
4 : 1
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