Which of the following represents a standing wave?

(1) $y=A \sin (\omega t-kx)$

(2) $y=A{e}^{-bx} \sin (\omega t-kx+\alpha )$

(3) $y=A \sin kx \sin (\omega t-\theta )$

(4) $y=(ax+b ) \sin (\omega t-kx)$

The equation of a standing wave in a stretched string is given by $\mathrm{y}=5 \sin \left(\frac{\mathrm{\pi x}}{3}\right) \cos \left(40\mathrm{\pi t}\right)$ where x and y are in cm and t is in seconds. The separation (in cm) between two consecutive nodes is:

(1) 1.5

(2) 3

(3) 6

(4) 4

In a stationary wave:

(1) Strain is maximum at nodes

(2) Strain is minimum at nodes

(3) Strain is maximum at antinodes

(4) Amplitude is zero at all points

In the standing wave shown, the particles at positions A and B have a phase difference of:

(1) 0

(2) $\frac{\pi }{2}$

(3) $\frac{5\pi }{6}$

(4) $\pi$

A 12 m long vibrating string has the speed of wave 48 m/s. To what frequency it will resonate?

(1) 2 cps

(2) 4 cps

(3) 6 cps

(4) All of these

A certain string will resonate to several frequencies, the lowest of which is 200 cps. What are the next three higher frequencies to which it resonates?

(1) 400, 600, 800

(2) 300, 400, 500

(3) 100, 150, 200

(4) 200, 250, 300

The length of a sonometer wire is 0.75 m and density 9 x 10³ Kg/m³. It can bear the stress of 8.1 x 10⁸ N/m² without exceeding the elastic limit. The fundamental frequency that can be produced in the wire is:

(1) 200 Hz

(2) 150 Hz

(3) 600 Hz

(4) 450 Hz

The string of a violin has a frequency of 440 cps. If the violin string is shortened by one fifth, its frequency will be changed to:

(1) 440 cps

(2) 880 cps

(3) 550 cps

(4) 2200 cps

A wire of length one metre under a certain initial tension emits a sound of fundamental frequency 256 Hz. When the tension is increased by 1 kg-wt, the frequency of the fundamental node increases to 320 Hz. The initial tension is:

(1) 3/4 kg wt

(2) 4/3 kg wt

(3) 16/9 kg wt

(4) 20/9 kg wt

In the case of a closed pipe which harmonic the p^th overtone will be:

(1) 2p + 1

(2) 2p -1

(3) p + 1

(4) p - 1