Advertisements
Advertisements
प्रश्न
The transverse displacement of a string (clamped at its both ends) is given by
y(x, t) = 0.06 sin `2/3` x cos (120 πt)
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is `3.0 xx 10^(-2)` kg.
Answer the following :
Determine the tension in the string.
उत्तर १
The given equation is y(x, t) = 0.06 sin `(2π)/3 xx` cos 120 πt …(1)
Velocity of transverse waves is
`"v" = sqrt("T"/"m") or "v"^2 = "T"/"m"`
`"T" = "mv"^2, "where m" = (3xx10^(-2))/1.5 = 2xx10^(-2) "kg/m"`
`:. "T" = (180)^2 xx 2 xx 10^(-2)`
= 648 N
उत्तर २
The velocity of a transverse wave travelling in a string is given by the relation:
`v = sqrt("T"/mu)` ...(i)
Where,
Velocity of the transverse wave, v = 180 m/s
Mass of the string, m = 3.0 × 10–2 kg
Length of the string, l = 1.5 m
Mass per unit length of the string, `mu = "m"/l`
`= 3.0/1.5 xx 10^(-2)`
`= 2xx 10^(-2) "kg m"^(-1)`
Tension in the string = T
From equation (i), tension can be obtained as:
T = v2μ
= (180)2 × 2 × 10–2
= 648 N
APPEARS IN
संबंधित प्रश्न
A travelling harmonic wave on a string is described by
`y(x,t) = 7.5 sin (0.0050x + 12t + pi/4)`
(a) What are the displacement and velocity of oscillation of a point at x = 1 cm, and t =1 s? Is this velocity equal to the velocity of wave propagation?
(b) Locate the points of the string which have the same transverse displacements and velocity as the x = 1 cm point at t = 2 s, 5 s and 11 s.
Draw a diagram to show the standing pressure wave and standing displacement wave for the 3rd overtone mode of vibration of an open organ pipe.
The transverse displacement of a string (clamped at its both ends) is given by
y(x, t) = 0.06 sin `2/3` x cos (120 πt)
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 × 10-2 kg.
Answer the following:
Does the function represent a travelling wave or a stationary wave?
The transverse displacement of a string (clamped at its both ends) is given by
y(x, t) = 0.06 sin `2/3` x cos (120 πt)
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 × 10-2 kg.
Answer the following:
Interpret the wave as a superposition of two waves travelling in opposite
directions. What is the wavelength, frequency, and speed of each wave?
A transverse harmonic wave of amplitude 0.01 m is generated at one end of a long horizontal string by a tuning fork of frequency 500 Hz. At a given instant of time, the displacement of a particle at a distance of 0.2 m from the fork is – 0.005 m and that of a particle at a distance of 0.1 m is + 0.005 m. The wavelength is
The equation of a simple harmonic progressive wave is given by y = A sin (100πt − 3x). Find the distance between 2 particles having a phase difference of `π/3`.
In the given progressive wave y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the amplitude.
In the given progressive wave y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the frequency.
In the given progressive wave y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the wave velocity.
In the given progressive wave y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the particle velocity amplitude..
