The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:

1.	\(3:1\)	2.	\(1:2\)
3.	\(2:1\)	4.	\(1:3\)

A string of length \(l\) is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is \(2\) mm. The amplitude of a particle at a distance \(l/8\) from the fixed end is:
        
1. \(2\sqrt2~\text{mm}\)
2. \(4~\text{mm}\)
3. \(\sqrt2~\text{mm}\)
4. \(2\sqrt3~\text{mm}\)

A pipe, \(30.0\) cm long, is open at both ends.

Take the speed of sound in air as \(330\) m s^–1.

The given diagram shows the progression of a harmonic wave from time t to t + $∆t$ where the crest of the wave displaces by $∆x$ . Then the speed of the wave will be:

$1. \frac{∆t}{∆x}$
$2. \frac{2∆x}{∆t}$
$3. \frac{∆x}{∆t}$
$4. \frac{2∆t}{∆x}$
$$

A rocket is moving at a speed of \(200\) ms^–1 towards a stationary target. While moving, it emits a wave of frequency \(1000\) Hz. Some of the sound reaching the target gets reflected back to the rocket as an echo. The frequency of the sound as detected by the target and the frequency of the echo as detected by the rocket respectively are: (speed of sound = \(330\) m/s)
1. \(4080\) Hz and \(2540\) Hz
2.  \(1000\) Hz and \(1000\) Hz
3.  \(2540\) Hz and \(4080\) Hz
4.  \(2540\) Hz and \(2540\) Hz