Advertisements
Advertisements
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?
उत्तर १
a) Mass of the wire, m = 3.5 × 10–2 kg
Linear mass density, `mu = m/l = 4.0 xx 10^(-2) kg m^(-1)`
Frequency of vibration, ν = 45 Hz
:. Length of the wire, `l = m/mu = (3.5xx10^(-2))/(4.0xx10^(-2)) = 0.875 m`
The wavelength of the stationary wave (λ) is related to the length of the wire by the relation:
`lambda = (2l)/n`
Where n = number of nodes in the wire
For fundamental node, n = 1:
λ = 2l
λ = 2 × 0.875 = 1.75 m
The speed of the transverse wave in the string is given as:
v = νλ= 45 × 1.75 = 78.75 m/s
b) The tension produced in the string is given by the relation:
T = v2µ
= (78.75)2 × 4.0 × 10–2 = 248.06 N
उत्तर २
Here n= 45 Hz, M = `3.5 xx 10^(-2)` kg
Mass per unit length = `m = 4.0 xx 10^(-2) kg m^(-1)`
`:. l = M/m = (3.5xx10^(-2))/(4.0xx10^(-2)) = 7/8`
As `l/2 = lambda = 7/8 :. lambda = 7/4 m = 1.75 m`
a) The speed of the transverse wave,` v = vlambda = 45 xx 1.75 = 78.75 "m/s"`
b) As ` v = sqrt(T/m)`
`:. T = v^2xx m = (78.75)^2xx 4.0 xx 10^(-2) = 248.06 N`
APPEARS IN
संबंधित प्रश्न
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'
A wave propagates on a string in the positive x-direction at a velocity \[\nu\] \[t = t_0\] is given by \[g\left( x, t_0 \right) = A \sin \left( x/a \right)\]. Write the wave equation for a general time t.
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 steel wire fixed at both ends has a fundamental frequency of 200 Hz. A person can hear sound of maximum frequency 14 kHz. What is the highest harmonic that can be played on this string which is audible to the person?
The string of a guitar is 80 cm long and has a fundamental frequency of 112 Hz. If a guitarist wishes to produce a frequency of 160 Hz, where should the person press the string?
A man standing unsymmetrical position between two mountains and fires a gun. He hears the first echo after 1.5 s and the second echo after 2.5 s. If the speed of sound in air is 340 m/s, then the distance between the mountains will be ______
What is the interference of sound waves?
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.
If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.
The displacement y of a particle in a medium can be expressed as, y = `10^-6sin(100t + 20x + pi/4)` m where t is in second and x in meter. The speed of the wave is ______.
