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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?

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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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पाठ 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]
पाठ 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


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


Explain why (or how) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases


Explain the reflection of transverse and longitudinal waves from a denser medium and a rared medium.


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.


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 particle on a stretched string supporting a travelling wave, takes 5⋅0 ms to move from its mean position to the extreme position. The distance between two consecutive particles, which are at their mean positions, is 2⋅0 cm. Find the frequency, the wavelength and the wave speed.


A steel wire of length 64 cm weighs 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it?


Consider the following statements about sound passing through a gas.
(A) The pressure of the gas at a point oscillates in time.
(B) The position of a small layer of the gas oscillates in time.


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


A heavy but uniform rope of length L is suspended from a ceiling. (a) Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower end. (b) If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling? (c) A particle is dropped from the ceiling at the instant the bottom end is given the jerk. Where will the particle meet the pulse?


Three resonant frequencies of a string are 90, 150 and 210 Hz. (a) Find the highest possible fundamental frequency of vibration of this string. (b) Which harmonics of the fundamental are the given frequencies? (c) Which overtones are these frequencies? (d) If the length of the string is 80 cm, what would be the speed of a transverse wave on this string?


The equation of a standing wave, produced on a string fixed at both ends, is
\[y = \left( 0 \cdot 4  cm \right)  \sin  \left[ \left( 0 \cdot 314  {cm}^{- 1} \right)  x \right]  \cos  \left[ \left( 600\pi  s^{- 1} \right)  t \right]\]
What could be the smallest length of the string?


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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