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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?

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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 Volume 1 and 2 [English]
अध्याय 15 Wave Motion and Waves on a String
Exercise | Q 34 | पृष्ठ ३२६

संबंधित प्रश्न

When longitudinal wave is incident at the boundary of denser medium, then............................

  1. compression reflects as a compression.
  2. compression reflects as a rarefaction.
  3. rarefaction reflects as a compression.
  4. longitudinal wave reflects as transverse wave.

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


A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?


A transverse harmonic wave on a string is described by y(x, t) = 3.0 sin (36 t + 0.018 x + π/4) 

Where x and y are in cm and t in s. The positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave?

If it is travelling, what are the speed and direction of its propagation?

(b) What are its amplitude and frequency?

(c) What is the initial phase at the origin?

(d) What is the least distance between two successive crests in the wave?


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


You are walking along a seashore and a mild wind is blowing. Is the motion of air a wave motion?


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.


A wave moving in a gas


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.


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.


A transverse wave of amplitude 0⋅50 mm and frequency 100 Hz is produced on a wire stretched to a tension of 100 N. If the wave speed is 100 m s−1, what average power is the source transmitting to the wire?


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?


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


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