The length of the string of a musical instrument is \(90\) cm and has a fundamental frequency of \(120\) Hz. Where should it be pressed to produce a fundamental frequency of \(180\) Hz? 

1.	\(75\) cm	2.	\(60\) cm
3.	\(45\) cm	4.	\(80\) cm

A wave travelling along a string is described by, \(y(x,t)=0.005 \text{ sin}(80.0x-3.0t),\) in which the numerical constants are in SI units. The wavelength and the period of the wave respectively are: 
1. \(7.85 ~\text{cm}\) and \(2.09 ~\text{s}\)
2. \(7.85 ~\text{cm}\) and \(1.09 ~\text{s}\)
3. \(7.85 ~\text{cm}\) and \(0.09 ~\text{s}\)
4. none of these

A wave travelling along a string is described by, \(y(x,~t)=0.005 ~\sin(80.0x-3.0t),\) in which the numerical constants are in SI units. The displacement \(y\) of the wave at a distance \(x = 30.0~\text {cm}\) and time \(t=20~\text{s}\) is:
1. \(0.5~\text{mm}\)
2. \(5~\text{mm}\)
3. \(5~\text{m}\)
4. \(5~\text{cm}\)

A steel wire \(0.72~\text{m}\) long has a mass of \(5\times10^{-3}~\text{kg}\). If the wire is under tension of \(60~\text{N}\), the speed of transverse waves on the wire will be:
1. \(85~\text{m/s}\)
2. \(83~\text{m/s}\)
3. \(93~\text{m/s}\)
4. \(100~\text{m/s}\)

The speed of sound in air at standard temperature and pressure is:
(Given the mass of \(1\) mole of air is \(29.0\times10^{-3}~\text{kg}\) and $\mathrm{}$\(\gamma=7/5 \text)\)
1. \(240 ~\text{m/s}\) 
2. \(331.5~\text{m/s}\) 
3. \(384.5~\text{m/s}\) 
4. \(280~\text{m/s}\) 

Two sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency \(5\) Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease to \(3\) Hz. What is the original frequency of B if the frequency of A is \(427\) Hz?
1. \(432\) Hz
2. \(424\) Hz
3. \(430\) Hz
4. \(422\) Hz

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

The following statements are given for a stationary wave:

a. Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.

b. All the particles cross their mean position at the same time.

c. All the particles are oscillating with the same amplitude.

d. There is no net transfer of energy across any plane.

e. There are some particles that are always at rest.

Choose the correct alternatives:

1. (a, b, d, e)

2. (a, c, d, e)

3. (b, c, d)

4. (c, d, e)

A train standing in a yard blows a whistle of frequency 400Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/s. Given that the speed of sound in still air is 340 m/s. Read the following statements.

(a) the frequency of sound as heard by an observer standing on the platform is 400Hz.

(b) the speed of sound for the observer standing on the platform is 350 m/s.

(c) the frequency of sound as heard by the observer standing on the platform will increase.

(d) the frequency of sound as heard by the observer standing on the platform will decrease.

Choose the correct alternatives:

1. (a, b)

2. (a, c)

3. (b, c)

4. (c, d)

The transverse displacement of a string (clamped at both ends) is given by $\mathrm{y}(\mathrm{x},\mathrm{t})=0.06\sin \left(\frac{2\mathrm{\pi x}}{3}\right)\cos \left(120\mathrm{\pi t}\right)$. All the points on the string between two consecutive nodes vibrate with:

(a) same frequency.

(b) same phase.

(c) same energy.

(d) different amplitude.

Choose the correct alternatives:

1. (a, b, d)

2. (a, c)

3. (b, d)

4. (c, d)