Advertisements
Advertisements
प्रश्न
A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C = 343 m s–1.
Advertisements
उत्तर १
Length of the steel wire, l = 12 m
Mass of the steel wire, m = 2.10 kg
Velocity of the transverse wave, v = 343 m/s
Mass per unit length, `mu = m/l = 2.10/12 = 0.175 kg m^(-1)`
For tension T, velocity of the transverse wave can be obtained using the relation:
`v = sqrt(T/mu)`
`:. T = v^2mu`
= (343)2 × 0.175 = 20588.575 ≈ 2.06 × 104 N
उत्तर २
Here l = 12.0 m, M = 2.10 kg
v = `343 "ms"^(-1)`
Mass per unit length = `M/l = 2.10/12.0 = 0.175 "kg m"^(-1)`
As `v = sqrt(T/m)`
`:. T = v^2. m = (343)^2 xx 0.175 = 2.06 xx 10^(4) N`
संबंधित प्रश्न
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10–2 kg and its linear mass density is 4.0 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?
Show that for a wave travelling on a string
\[\frac{y_{max}}{\nu_{max}} = \frac{\nu_{max}}{\alpha_{max}},\]
where the symbols have usual meanings. Can we use componendo and dividendo taught in algebra to write
\[\frac{y_{max} + \nu_{max}}{\nu_{max} - \nu_{max}} = \frac{\nu_{max} + \alpha_{max}}{\nu_{max} - \alpha_{max}}?\]
A sine wave is travelling in a medium. The minimum distance between the two particles, always having same speed, is
Two strings A and B, made of same material, are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed `v_A` and on B with speed `v_B`. The ratio `v_A/v_B` is ______.
A wave pulse, travelling on a two-piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to the incident one. If the incident wave has wavelength λ and the transmitted wave λ'
Two wave pulses travel in opposite directions on a string and approach each other. The shape of one pulse is inverted with respect to the other.
The equation of a wave travelling on a string stretched along the X-axis is given by
\[y = A e {}^- \left( \frac{x}{a} + \frac{t}{T} \right)^2 .\]
(a) Write the dimensions of A, a and T. (b) Find the wave speed. (c) In which direction is the wave travelling? (d) Where is the maximum of the pulse located at t = T? At t = 2 T?
The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is v. Write the wave equation.
The equation of a wave travelling on a string is:
\[y = \left( 0 \cdot 10 \text{ mm } \right) \sin\left[ \left( 31 \cdot 4 m^{- 1} \right)x + \left( 314 s^{- 1} \right)t \right]\]
- In which direction does the wave travel?
- Find the wave speed, the wavelength and the frequency of the wave.
- What is the maximum displacement and the maximum speed of a portion of the string?
Two long strings A and B, each having linear mass density
\[1 \cdot 2 \times {10}^{- 2} kg m^{- 1}\] , are stretched by different tensions 4⋅8 N and 7⋅5 N respectively and are kept parallel to each other with their left ends at x = 0. Wave pulses are produced on the strings at the left ends at t = 0 on string A and at t = 20 ms on string B. When and where will the pulse on B overtake that on A?
A 40 cm wire having a mass of 3⋅2 g is stretched between two fixed supports 40⋅05 cm apart. In its fundamental mode, the wire vibrates at 220 Hz. If the area of cross section of the wire is 1⋅0 mm2, find its Young modulus.
Following figure shows a string stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a particular tuning for. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the density of the material of the block.
A string 1 m long is fixed at one end. The other end is moved up and down with a frequency of 20 Hz. Due to this, a stationary wave with four complete loops gets produced on the string. Find the speed of the progressive wave which produces the stationary wave.
Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with temperature.
For the travelling harmonic wave
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)
Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 0.5 m.
A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions ______.
A transverse harmonic wave on a string is described by y(x, t) = 3.0 sin (36t + 0.018x + π/4) where x and y are in cm and t is in s. The positive direction of x is from left to right.
- The wave is travelling from right to left.
- The speed of the wave is 20 m/s.
- Frequency of the wave is 5.7 Hz.
- The least distance between two successive crests in the wave is 2.5 cm.
Speed of sound waves in a fluid depends upon ______.
- directty on density of the medium.
- square of Bulk modulus of the medium.
- inversly on the square root of density.
- directly on the square root of bulk modulus of the medium.
A wave of frequency υ = 1000 Hz, propagates at a velocity v = 700 m/sec along x-axis. Phase difference at a given point x during a time interval M = 0.5 × 10-3 sec is ______.
