A wave represented by the given equation $y=a\cos (kx-\omega t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is :

(1) $y=a\sin (kx+\omega t)$

(2) $y=-a\cos (kx+\omega t)$

(3) $y=-a\cos (kx-\omega t)$

(4) $y=-a\sin (kx-\omega t)$

A standing wave is represented by

$Y=A\sin \left(100t\right)\cos (0.01x)$

where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :

(1) 10⁴ m/s

(2) 1 m/s

(3) 10^–4 m/s

(4) Not derivable from the above data

A 1 cm long string vibrates with the fundamental frequency of 256 Hz. If the length is reduced to $\frac{1}{4}cm$  keeping the tension unaltered, the new fundamental frequency will be :

(1) 64

(2) 256

(3) 512

(4) 1024

The tension in a piano wire is 10N. What should be the tension in the wire to produce a note of double the frequency :

(1) 5 N

(2) 20 N

(3) 40 N

(4) 80 N

A second harmonic has to be generated in a string of length l stretched between two rigid supports. Distances from one end where the string has to be plucked and touched are :

(1) Plucked at $\frac{l}{4}$ and touched at $\frac{l}{2}$

(2) Plucked at $\frac{l}{4}$ and touched at $\frac{3l}{4}$

(3) Plucked at $\frac{l}{2}$ and touched at $\frac{l}{4}$

(4) Plucked at $\frac{l}{2}$ and touched at $\frac{3l}{4}$

A tube closed at one end and containing air is excited. It produces the fundamental note of frequency of 512 Hz. If the same tube is open at both the ends the fundamental frequency that can be produced is :

(1) 1024 Hz

(2) 512 Hz

(3) 256 Hz

(4) 128 Hz

An empty vessel is getting filled with water, then the frequency of vibration of the air column in the vessel 

(1) Remains the same

(2) Decreases

(3) Increases

(4) First increases then decrease

If the velocity of sound in air is 336 m/s. The maximum length of a closed pipe that would produce a just audible sound will be : 

(1) 3.2 cm

(2) 4.2 m

(3) 4.2 cm

(4) 3.2 m

The frequency of fundamental tone in an open organ pipe of length 0.48 m is 320 Hz. The speed of sound is 320 m/sec. Frequency of fundamental tone in closed organ pipe will be : 

1. 153.8 Hz

2. 160.0 Hz

3. 320.0 Hz

4. 143.2 Hz

An open pipe of length l vibrates in the fundamental mode. The pressure variation is maximum at :

(1) l/4 from ends

(2) The middle of the pipe

(3) The ends of the pipe

(4) At l/8 from ends of pipe