51.

A string of density 7.5 g cm³ and area of cross-section 0.2 mm² is stretched under a tension of 20 N. When it is plucked at the mid-point, the speed of the transverse wave on the wire is

• 116 ms^-1

• 40 ms^-1

• 200 ms^-1

• 80 ms^-1

In a gas, two waves of wavelengths 1 m and 1.01 m are superposed and produce 10 beats in 3 s. The velocity of sound in the medium is

• 300 m/s

• 336.7 m/s

• 360.2 m/s

• 270 m/s

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 os 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 that of the first, frequency of the second tuning fork is

• 138 Hz

• 132 Hz

• 144 Hz

• 276 Hz

The equation $\mathrm{y} = \mathrm{A} \sin 2\mathrm{\pi } \left(\frac{\mathrm{t}}{\mathrm{T}} - \frac{\mathrm{x}}{\mathrm{\lambda }}\right)$, 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 (λ/T)

• velocity in negative x-direction

A pipe open at both the ends produce 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 tuning fork of frequency 580 Hz is employed to produce transverse waves on a long rope. The distance between the nearest crusts is found to be 20 cm. The velocity of the wave is

• 58 ms^-1

• 580 ms^-1

• 116 ms^-1

• 29 ms^-1

The distance travelled by a sound wave when a tuning fork completes 25 vib in 16.5 m. If the frequency of the tuning fork is 500 Hz, find the velocity of sound.

• 350 ms^-1

• 330 ms^-1

• 300 ms^-1

• 450 ms^-1

Two instruments having stretched strings are being played in unison. When the tension of one of the instruments is increased by 1 %, 3 beats are produced in 2s. The initial frequency of vibration of each wire is

• 300 Hz

• 500 Hz

• 1000 Hz

• 400 Hz