Two vibrating strings of the same material but  lengths L and 2 L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency v₁ and the other with frequency v₂ . The ratio v₁ / v₂ is

• 2

• 4

• 8

• 1

The equation $y = A \sin 2\mathrm{\pi } \left(\frac{\mathrm{t}}{\mathrm{T}} - \frac{\mathrm{x}}{\mathrm{\lambda }}\right)$ where the symbols carry the usual meaning and A, T and λ are positive, represents a wave of

• amplitude 2 A

• period T/λ

• speed xλ

• speed $\left(\frac{\mathrm{\lambda }}{\mathrm{T}}\right)$

A pipe open at both the ends produces a note of fundamental frequency f₁ . When the pipe is kept with $\frac{3}{4}$th of its length in water, it produces a note of fundamental frequency f₂ . The ratio of  $\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}$ is

• $\frac{4}{3}$

• $\frac{3}{4}$

• 2

• $\frac{1}{2}$

A red coloured object illuminated by mercury vapour lamp, when seen through a green filter, will appear

• red

• blue

• violet

• black

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is

• 1 : 1

• 2 : 1

• 1 : 4

• 1 : 2

An observer standing near the sea shore 54 min. If the wavelength of the water wave is 10 m, then the velocity of water wave is

• 540 ms^-1

• 5.4 ms^-1

• 0.184 ms^-1

• 9 ms^-1

A set of 24 tuning forks are so arranged that each gives 6 beats/s with the previous one. If the frequency of the last tuning fork is double than that of the first, frequency of the second tuning fork is

• 138 Hz

• 132 Hz

• 144 Hz

• 276 Hz

The equation of a progressive wave can be given by y = 15 sin (660 − 0.02 $\mathrm{\pi }$x) cm. The frequency of the wave is

• 330 Hz

• 342 Hz

• 365 Hz

• 660 Hz

A hollow cylinder with both sides open generates a frequency f in air. When the cylinder vertically immersed into water by half its length the frequency will be

• f

• 2f

• f/2

• f/4

Two stretched strings have lengths land 2l while tension are T and 4 T respectively. If they are made of same material the ratio of their frequency is

• 2 : 1

• 1 : 2

• 1 : 1

• 1 : 4