A train whistling at constant frequency is moving towards a station at a constant speed v. The train goes past a stationary observer on the station. The frequency n' of the sound as heard by the observer is plotted as a function of time t (figure). Identify the expected curve.

1.                           2.  

3.                            4. 

A transverse harmonic wave on a string is described by
                   $\mathrm{y}\left(\mathrm{x},\mathrm{t}\right)=3.0\sin \left(36\mathrm{t}+0.018\mathrm{x}+\frac{\mathrm{\pi }}{4}\right)$
where x and y are in cm and t is in sec. The positive direction of x is from left to right.

(a) The wave is travelling from right to left.

(b) The speed of the wave is 20 m/s.

(c) The frequency of the wave is 5.7 Hz.

(d) The least distance between two successive crests in the wave is 2.5 cm.

Choose the correct alternatives:

1. (a, b, d)

2. (a, b, c)

3. (b, c, d)

4. (a, c, d)

The displacement of the string is given by,
                             $\mathrm{y}\left(\mathrm{x},\mathrm{t}\right)=0.06\sin \left(\frac{2\mathrm{\pi x}}{3}\right)\cos \left(120\mathrm{\pi t}\right)$
where x and y are in metres and t in seconds. The length of the string is 1.5 m and its mass is $3.0\times {10}^{-2} \mathrm{kg}.$

(a) It represents a progressive wave of frequency 60 Hz.

(b) It represents a stationary wave of frequency 60 Hz.

(c) It is the result of a superposition of two waves of wavelength 3 m, frequency 60 Hz each travelling with a speed of 180 m/s in the opposite direction.

(d) The amplitude of this wave is constant.

Choose the correct alternatives:
1. (b), (d)
2. (a), (c)
3. (b), (c)
4. (c), (d)

The speed of sound in a fluid depends upon 

(a) directly on the density of the medium.

(b) square of the Bulk modulus of the medium.

(c) inversely on the square root of density.

(d) directly on the square root of the bulk modulus of the medium.
 

Choose the correct alternatives:
1. (a, b)

2. (a, c)

3. (b, d)

4. (c, d)

During the propagation of a plane progressive mechanical wave,

(a) all the particles are vibrating in the same phase.

(b) the amplitude of all the particles is equal.

(c) the particles of the medium execute SHM.

(d) the wave velocity depends upon the nature of the medium.

Choose the correct alternatives:

1. (a, b, d)

2. (a, c)

3. (b, c, d)

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)

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 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 string of mass 2.5 kg is under the tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in:

1. 1 s

2. 0.5 s

3. 2 s

4. data given is insufficient

Equation of a plane progressive wave is given by $y=0.6 \sin 2\mathrm{\pi }\left(\mathrm{t}-\frac{x}{2}\right)$. On reflection from a denser medium, its amplitude becomes  $\frac{2}{3}$rd of the amplitude of the incident wave. The equation of the reflected wave is:

1. $\mathrm{y}=0.6 \sin 2\mathrm{\pi }\left(\mathrm{t}+\frac{\mathrm{x}}{2}\right)$

2. $\mathrm{y}=-0.4 \sin 2\mathrm{\pi }\left(\mathrm{t}+\frac{\mathrm{x}}{2}\right)$

3. $\mathrm{y}=0.4 \sin 2\mathrm{\pi }\left(\mathrm{t}+\frac{\mathrm{x}}{2}\right)$

4. $\mathrm{y}=-0.4 \sin 2\mathrm{\pi }\left(\mathrm{t}-\frac{\mathrm{x}}{2}\right)$