Superposition of Waves
Superposition of Waves
- The fundamental frequency of a pipe closed at one end is 250 Hz. The frequency of its first overtone is Answer: D. 750 Hz A closed pipe has only odd harmonics; first overtone =3n=750 Hz. 1
- A tuning fork of frequency 256 Hz produces 4 beats/s with an unknown fork. When the unknown fork is loaded with a little wax (which lowers its frequency), the number of beats becomes 6 per second. The original frequency of the unknown fork is Answer: A. 252 Hz Unknown is 252 or 260 Hz. Loading lowers frequency; beats increase only if it was already below 256, so it is 252 Hz. 1
- A string 1 m long, fixed at both ends, carries transverse waves with speed 200 m/s. The frequency of its second overtone is Answer: A. 300 Hz Fundamental =v/2L=100 Hz; second overtone = third harmonic =300 Hz. 1
- A wave of frequency 500 Hz is travelling with a speed of 350 m/s. Given: n = 500 Hz, v = 350 m/s V = n x λ ∴ λ = 350/500 = 0.7 m (a) in t = 1.0 ms = 0.001 s, the path difference is the distance covered v x... 1
- A sound wave in a certain fluid medium is reflected at an obstacle to form a standing wave. Given : Distance between two successive nodes = λ/2 = 3.75 x 10⁻² m, v =1500 m/s ∴ λ = 7.5 x 10⁻² m v = n x λ ∴ n = v/λ = frac15003.75×10⁻²... 1
- Two sources of sound are separated by a distance 4 m. They both emit sound with the same amplitude and frequency (330 Hz ∴ λ = v/n = 330/330 = 1 m Directly at the cenre of two sources of sound, path difference is zero. But since the waves are 180° out of phase,... 1
- Two sound waves travel at a speed of 330 m/s. If their frequencies are also identical and are equal to 540 Hz Given: n₁ = n₂ = 540 Hz, v = 330 m/s V = n x λ ∴ λ = 330/540 = 0.61 m Here the path difference = 3.5 – 3 = 0.5 m ∴ Phase difference = 2π/λ x... 1
- Two wires of the same material and same cross section are stretched on a sonometer. Given : m₁ = m₂ = m, L₁ = 60 cm = 0.6 m, T₁ = 1.5 kg=14.7 N, T₂ =6 kg=58.8 N n₁ = 1/2L₁√(T₁/m) and n₂ = 1/2L₂√(T₂/m) But n_(1 )= n₂ ∴ 1/2L₁√... 1
- A pipe closed at one end can produce overtones at frequencies 640 Hz, 896 Hz and 1152 Hz. The difference between the given frequencies of the overtones is 256 Hz. This implies that they are consecutive overtones. Let n_c be the fu... 1
- A standing wave is produced in a tube open at both ends. The fundamental frequency is 300 Hz. What is the length of tube Given : For the tube open at both the ends, n = 300 Hz and v = 340 m / s ignoring end correction, the fundamental frequency of the tube is n... 1
- Find the fundamental, first overtone and second overtone frequencies of a pipe, open at both the end Given : Open pipe, L= 25 cm = 0.25 m, v = 330 m/s The fundamental frequency of an open pipe ignoring end correction, n_(O )= v/λ = v/2L ∴ n_... 1
- A pipe open at both the ends has a fundamental frequency of 600 Hz. Given : Open pipe, n_o = 600 Hz, n_c 1 = n_o 1 (first overtones) For an open pipe, the fundamental frequency, n_O = v/2Lo The length of the o... 1
- A string 1m long is fixed at one end. The other end is moved up and down with frequency 15 Hz. Given : L = 1 m, n = 15 Hz. The string is fixed only at one end. Hence, an antinode will be formed at the free end. Thus, with four and half... 1
- A violin string vibrates with fundamental frequency of 440Hz. What are the frequencies of first and second overtones? Given : n = 440 Hz The first overtone, n₁ = 2n = 2 x 400 = 880 Hz The second overtone, n₂ = 3n = 3 x 400 = 1320 Hz 1
- A set of 8 tuning forks is arranged in a series of increasing order of frequencies. Given : n₈ = 2 n₁, beat frequency = 4 Hz The set of tuning fork is arranged in the increasing order of their frequencies. ∴ n₂ = n_(1 )+ 4 n... 1
- A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. Given : L= 0.5 m, T = 5kg = 5 x 9.8 = 49N, n = 100 Hz n = 1/2L√(T/m) ∴ Linear density, m = T/4L²n² = 49/4(0.5)²(100)² = 4.9 x 10⁻³ kg/m 1
- The string of a guitar is 80 cm long and has a fundamental frequency of 112 Hz. Given: L₁ = 80 cm n₁ = 112 Hz, n₂ =160 Hz According to the law of length, n₁L₁ = n₂L₂. The vibrating length to produce the fundamental frequ... 1
- Derive an expression for equation of stationary wave on a stretched string. When two progressive waves having the same amplitude, wavelength and speed propagate in opposite directions through the same region of a med... 1
- State the characteristics of stationary waves. Characteristics of stationary waves : Stationary waves are produced due to superposition of two identical waves (either transverse or longit... 1
- State the characteristics of progressive waves. Characteristics of progressive waves: 1) Each particle in a medium executes the same type of vibration. Particles vibrate about their mean p... 1
- What are harmonics and overtones? A stationary wave is set up in a bounded medium in which the boundary could be a rigid support (i.e., a fixed end, as for instance a string... 1
- A wave is represented by an equation y =A sin (Bx + Ct). Given that the constants A, B and C are positive When a wave represented by an equation y=Asin(Bx+Ct) with the positive constants A, B and C, then, the incident wave is travelling along (-v... 1
- A standing wave is produced on a string fixed at one end with the other end free. The length of the string (A) must be an odd integral multiple of λ/4. 2
- Which of the following equations represents a wave travelling along the y-axis? (A) x = Asin (ky - ωt) 2