Advertisements
Advertisements
प्रश्न
A sonometer wire having a length of 1⋅50 m between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire?
Advertisements
उत्तर
Given:
Length of the sonometer wire (L) = 1.50 m
Let the
\[\text{ first harmonic be f_0 and thesecond harmonic be f_1 }.\]
According to the question,
\[f_1 = 256 \text{ Hz }\]
,\[\text{ 1st harmonic for fundamental frequency, f_0 = \frac{f_1}{2} = \frac{256}{2} = 128 Hz}\]
When the fundamental wave is produced, we have:
\[\frac{\lambda}{2} = 1 . 5 m\]
\[ \Rightarrow \lambda = 3 m\]
\[\text{ Wave speed, } v = f_0 \lambda\]
\[ \Rightarrow v = 128 \times 3 = 384 m/s\]
APPEARS IN
संबंधित प्रश्न
Light waves each of amplitude "a" and frequency "ω", emanating from two coherent light sources superpose at a point. If the displacements due to these waves are given by y1 = a cos ωt and y2 = a cos(ωt + ϕ) where ϕ is the phase difference between the two, obtain the expression for the resultant intensity at the point.
As you have learnt in the text, the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle?
A tuning fork of frequency 480 Hz is used to vibrate a sonometer wire having natural frequency 240 Hz. The wire will vibrate with a frequency of
A 4⋅0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of \[19 \cdot 2 \times {10}^{- 3} kg m^{- 1}\] . Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2⋅0 m s−2. Take g = 10 m s−2.
Two waves, each having a frequency of 100 Hz and a wavelength of 2⋅0 cm, are travelling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced 0⋅015 s later than the first one at the same place, (b) if the two waves were produced at the same instant but first one was produced a distance 4⋅0 cm behind the second one? (c) If each of the waves has an amplitude of 2⋅0 mm, what would be the amplitudes of the resultant waves in part (a) and (b) ?
The energy in the superposition of waves ____________.
If `sqrt("A"^2+"B"^2)` represents the magnitude of resultant of two vectors `(vec"A" + vec"B")` and `(vec"A" - vec"B")`, then the angle between two vectors is ______.
Two particles P and Q describe simple harmonic motions of same amplitude a, frequency v along the same straight line. The maximum distance between the two particles is a`sqrt(2)`. The initial phase difference between the particles is
Consider a ray of light incident from air onto a slab of glass (refractive index n) of width d, at an angle θ. The phase difference between the ray reflected by the top surface of the glass and the bottom surface is ______.
The displacement of an elastic wave is given by the function y = 3 sin ωt + 4 cos ωt. where y is in cm and t is in second. Calculate the resultant amplitude.
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of 0.5 m
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of `(3λ)/4` (at a given instant of time)
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of What is the phase difference between the oscillation of a particle located at x = 100 cm, at t = T s and t = 5 s?
The equations of two waves are given by :
y1 5 sin2π (x - vt) cm
y2 3 sin2π (x - vt + 1.5) cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is ______.
When two coherent monochromatic light beams of intensities I and 4I are superimposed, then what are the maximum and minimum possible intensities in the resulting beams?
