Tuning fork \(F_1\) has a frequency of \(256~\text{Hz}\) and it is observed to produce \(6\) beats/second with another tuning fork \(F_2\). When \(F_2\) is loaded with wax, it still produces \(6\) beats/second with \(F_1\). The frequency of \(F_2\) before loading was:
1. \(253~\text{Hz}\)
2. \(262~\text{Hz}\)
3. \(250~\text{Hz}\)
4. \(259~\text{Hz}\)

Beats are produced by two waves given by $y_1=a\sin 2000\pi t$ and $y_2=a\sin 2008\pi t$. The number of beats heard per second is :

(1) Zero

(2) One

(3) Four

(4) Eight

The distance between the nearest node and antinode in a stationary wave is :

(1) λ

(2) $\frac{\lambda }{2}$

(3) $\frac{\lambda }{4}$

(4) 2λ

For the stationary wave $y=4\sin \left(\frac{{\displaystyle \pi x}}{{\displaystyle 15}}\right)\cos \left(96\pi t\right)$, the distance between a node and the next antinode is :

1. 7.5

2. 15

3. 22.5

4. 30

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 $\frac{3l}{4}$