All questions
- 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
- The tension in a piano wire is increased by 25%. Its frequency becomes ….. times the original frequency. (B) 1.12 The tension in a piano wire is increased by 25%. Its frequency becomes 1.12 times the original frequency. 1
- If two open organ pipes of length 50 cm and 51 cm sounded together produce 7 beats per second, the speed of sound is. (D) 357m/s If two open organ pipes of length 50 cm and 51 cm sounded together produce 7 beats per second, the speed of sound is 357 m/s 1
- When an air column in a pipe closed at one end vibrates such that three nodes are formed in it (D) 5 The frequency of its vibrations is 5 times the fundamental frequency. 1
- Conventions for the use of SI Units: (1) Unit of every physical quantity should be represented by its symbol. (2) Full name of a unit always starts with smaller letter even if t... 1
- System of Units , types and examples (i) CGS: Centimetre Gram Second system (ii) MKS: Metre Kilogram Second system (iii) FPS: Foot Pound Second system. (iv) SI: System Internati... 1
- A wooden block of mass m is kept on a piston that Given : A = 0.25m, g = π² = 10 m s² During vertical oscillations, the acceleration is maximum at the turning points at the top and bottom. T... 1
- Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field Given: B =1.6 x 10⁻⁵ T, I = 3 x 10⁻⁶ Kg/m², m =3 A-m² The period of oscillation, T = 2π √(I/μB) ∴ The frequency of oscillation is η = 1/2π√(... 1
- A 20 cm wide thin circular disc of mass 200 g is suspended to a rigid support from a thin metallic string Given: R = 10cm = 0.1 m, M = 0.2 kg, θ_m=60⁰ = p/3 rad, T=1 s, π³ = 31 The MI of the disc about the rotation axis (perpendicular through its... 1
- Two parallel S.H.M.s represented by x1 = 5sin (4πt + π/3) cm and x2 = 3sin (4πt + π/4) cm are superposed Given : x₁ = 5sin (4πt + π/3) = A₁ sin(ωt + α), x₂ = 3sin (4πt + π/4) = A₂ sin(ωt + β), ∴ A₁ =5 cm, A₂ =3 cm, α = π/3 rad, β = π/4 rad (i) R... 1
- The displacement of an oscillating particle is given by x= a sin ωt + b cos ωt where a, b and ω are constant x= a sin ωt + b cos ωt Let a = A cos ∅ and b = A sin ∅, so that A² = a^(2 )+ b² and tan ∅ = b/a x=A cos ∅ sin ωt + A sin ∅ cos ωt x = A sin... 1
- The period of oscillation of a body of mass m1 suspended from a light spring is T. For mass m₁, period is T ∴ T = 2π √(m₁/k) For mass m₂, period is 2T ∴ 2T = 2π √(m₁+m₂/k) ∴ 2T/T = 2 = √(m₁+m₂/m₁) ∴ m₁+m₂/m₁ = 4 ∴ m₂/m₁ = 3... 1
- A particle performing linear S.H.M. of period 2p seconds Given : T = 2π s, v = b√(3) m/s at x=b ω = 2π/T = 2π/2π =1 rad/s v = ω √(A²-x²) ∴ at x = b, b√(3) = (1) √(A²-x²) ∴ 3b² = A² – b^(2 ), ∴ A =... 1
- At what distance from the mean position is the kinetic energy of a particle performing S.H.M. of amplitude 8 cm Given : A=8 cm, KE = 3PE KE = 1/2 k(A² —x²) and PE = 1/2 kx² Given, KE = 3PE. ∴ 1/2 k(A² —x²) = 3( 1/2 kx²) ∴ A² —x^(2 )= 3x^(2 ), ∴ 4x² = A... 1
- Find the change in length of a second’s pendulum, if the acceleration due to gravity at the place changes from 9.75 Given : g₁ =9.75 m/s², g₂ = 9.8 m/s² Length of a seconds pendulum, L = g/π² ∴ L₁ = g₁/π² = 9.75/9.872 = 0.9876 m and ∴ L₂ = g₂/π^(2 )= 9.8/9... 1
- A simple pendulum of length 100 cm performs S.H.M. Find the restoring force acting on its bob of mass Given : L = 100cm, m = 50 g = 5 x 10⁻² kg, x = 3 cm, g = 9.8 m/s² Restoring force, F = mg sin θ = mgθ = (5 x 10⁻²)(9.8)(3/100) = 1.48 x 10⁻²... 1