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If the Speed of a Transverse Wave on a Stretched String of Length 1 M is 60 M−1, What is the Fundamental Frequency of Vibration? - Physics

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प्रश्न

If the speed of a transverse wave on a stretched string of length 1 m is 60 m−1, what is the fundamental frequency of vibration?

योग
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उत्तर

Length of a stretched string (L) = 1 m
Wave speed (v) = 60 m/s
Fundamental frequency (f0) of vibration is given as follows:
\[f_0  = \frac{v}{2L}\] 

\[= \frac{60}{2} \times 1\] 

\[ = 30   s^{- 1}  = 30  \text{ Hz }\]

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अध्याय 15: Wave Motion and Waves on a String - Exercise [पृष्ठ ३२६]

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एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
अध्याय 15 Wave Motion and Waves on a String
Exercise | Q 34 | पृष्ठ ३२६

संबंधित प्रश्न

When a transverse wave on a string is reflected from the free end, the phase change produced is ..............

(a) zero rad

(b) ` pi/2 ` rad

(c) `(3pi)/4` rad

(d) `pi`  rad


Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a traveling wave, (ii) a stationary wave or (iii) none at all:

y = cos x sin t + cos 2x sin 2t


A mechanical wave propagates in a medium along the X-axis. The particles of the medium
(a) must move on the X-axis
(b) must move on the Y-axis
(c) may move on the X-axis
(d) may move on the Y-axis.


A transverse wave travels along the Z-axis. The particles of the medium must move


Longitudinal waves cannot


A wave going in a solid
(a) must be longitudinal
(b) may be longitudinal
(c) must be transverse
(d) may be transverse.


Figure shows a plot of the transverse displacements of the particles of a string at t = 0 through which a travelling wave is passing in the positive x-direction. The wave speed is 20 cm s−1. Find (a) the amplitude, (b) the wavelength, (c) the wave number and (d) the frequency of the wave.


Two wires of different densities but same area of cross section are soldered together at one end and are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.


A transverse wave described by \[y = \left( 0 \cdot 02  m \right)  \sin  \left( 1 \cdot 0  m^{- 1} \right)  x + \left( 30  s^{- 1} \right)t\] propagates on a stretched string having a linear mass density of \[1 \cdot 2 \times  {10}^{- 4}   kg   m^{- 1}\] the tension in the string.


Two blocks each having a mass of 3⋅2 kg are connected by a wire CD and the system is suspended from the ceiling by another wire AB (See following figure). The linear mass density of the wire AB is 10 g m−1 and that of CD is 8 g m−1. Find the speed of a transverse wave pulse produced in AB and CD.


An organ pipe, open at both ends, contains


In the arrangement shown in figure  , the string has a mass of 4⋅5 g. How much time will it take for a transverse disturbance produced at the floor to reach the pulley? Take g = 10 m s−2.


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A steel wire of mass 4⋅0 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N. Find the frequency and wavelength of the fourth harmonic of the fundamental.


A wire, fixed at both ends is seen to vibrate at a resonant frequency of 240 Hz and also at 320 Hz. (a) What could be the maximum value of the fundamental frequency? (b) If transverse waves can travel on this string at a speed of 40 m s−1, what is its length?


The equation of a standing wave, produced on a string fixed at both ends, is
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What could be the smallest length of the string?


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y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)


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