1. Standing wave are formed on a stretched string under tension of 1
N. The length of the string is 30 cm and it vibrates in 3 loops. If the
mass per unit length of wire is 10 mg/cm, calculate the frequency of
the vibrations. Get solution
2. In the above problem, if the string is made to vibrate in its fundamental mode, what will be the frequency of vibration? Get solution
3. In the experimental arrangement of Wiener, what should be the angle between the film and the mirror if the distance between two consecutive dark bands is 7 × 10–3 cm. Assume λ = 6 × 10–5 cm. Get solution
4. Standing wave with five loops are produced on a stretched string under tension. The length of the string is 50 cm and the frequency of vibrations is 250 sec–1 . Calculate the time variation of the displacement of the points which are at distances of 2 cm, 5 cm, 15 cm, 18 cm, 20 cm, 35 cm and 45 cm from one end of the string. Get solution
5. The displacements associated with two waves (propagating in the same direction) having same amplitude but slightly different frequencies can be written in the form... and ...(such displacements are indeed obtained when we have two tuning forks with slightly different frequencies.) Discuss the superposition of the displacements and show that at a particular value of x, the intensity will vary with time. Get solution
6. In the above problem assume v = 330 m/sec, ν = 256 sec –1, Δν = 2 sec –1 and a = 0.1 cm. Plot the time variation of the intensity at x = 0 , ...and .... Get solution
7. Use the complex representation to study the time variation of the resultant displacement at x = 0 in Problems 13.5 and 13.6. Get solution
8. Discuss the superposition of two plane waves (of the same frequency and propagating in the same direction) as a function of the phase difference between them. (Such a situation indeed arises when a plane wave gets reflected at the upper and lower surfaces of a glass slab; see Sec. 15.2). Get solution
9. In Example 11.1 we had discussed the propagation of a semicircular pulse on a string. Consider two semicircular pulses propagating in opposite directions. At t =0, the displacement associated with the pulses propagating in the +x and in the –x directions are given by...and ...respectively. Plot the resultant disturbance at t = R/v, 2.5 R/v, 7.5 R/v and 10 R/v; where v denotes the speed of propagation of the wave. Get solution
2. In the above problem, if the string is made to vibrate in its fundamental mode, what will be the frequency of vibration? Get solution
3. In the experimental arrangement of Wiener, what should be the angle between the film and the mirror if the distance between two consecutive dark bands is 7 × 10–3 cm. Assume λ = 6 × 10–5 cm. Get solution
4. Standing wave with five loops are produced on a stretched string under tension. The length of the string is 50 cm and the frequency of vibrations is 250 sec–1 . Calculate the time variation of the displacement of the points which are at distances of 2 cm, 5 cm, 15 cm, 18 cm, 20 cm, 35 cm and 45 cm from one end of the string. Get solution
5. The displacements associated with two waves (propagating in the same direction) having same amplitude but slightly different frequencies can be written in the form... and ...(such displacements are indeed obtained when we have two tuning forks with slightly different frequencies.) Discuss the superposition of the displacements and show that at a particular value of x, the intensity will vary with time. Get solution
6. In the above problem assume v = 330 m/sec, ν = 256 sec –1, Δν = 2 sec –1 and a = 0.1 cm. Plot the time variation of the intensity at x = 0 , ...and .... Get solution
7. Use the complex representation to study the time variation of the resultant displacement at x = 0 in Problems 13.5 and 13.6. Get solution
8. Discuss the superposition of two plane waves (of the same frequency and propagating in the same direction) as a function of the phase difference between them. (Such a situation indeed arises when a plane wave gets reflected at the upper and lower surfaces of a glass slab; see Sec. 15.2). Get solution
9. In Example 11.1 we had discussed the propagation of a semicircular pulse on a string. Consider two semicircular pulses propagating in opposite directions. At t =0, the displacement associated with the pulses propagating in the +x and in the –x directions are given by...and ...respectively. Plot the resultant disturbance at t = R/v, 2.5 R/v, 7.5 R/v and 10 R/v; where v denotes the speed of propagation of the wave. Get solution
