String Open at One End

Q.

What is a phase in physics?

Q. If two waves represented by $y_1=4\sin \omega t$ and $y_2=3\sin (\omega t+\frac{\pi }{3})$ interfere at a point, the amplitude of the resulting wave will be close to

1. $5$
2. $6$
3. $3.5$
4. $4.5$

Q. A particle is subjected to two SHMs of displacement $x_1=5\sin (\omega t+{30}^{\circ })$ and $x_2=3\sin (\omega t+{120}^{\circ })$ respectively. Find out the amplitude of the resulting SHM.

1. $\sqrt{8}$
2. $\sqrt{34}$
3. $\sqrt{2}$
4. $\sqrt{15}$

Q. The equation of displacement of two waves are given as ; $y_1=10\sin (3\pi t+\frac{\pi }{3}),y_2=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)$. Then, what will be the ratio of their amplitudes?

1. $1:2$
2. $2:1$
3. $1:1$
4. None of these

Q.

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?

Q. In the line spectra of hydrogen atom, the difference between the largest and the shortest wavelength of the Lyman series is $304\mathring{A}$ The corresponding difference for the Paschen series (in $\mathring{A}$) is close to (upto two decimal places)

Q.

An open organ pipe is closed suddenly with the result, that the second overtone of the closed pipe is found to be higher in frequency by $100$ than the first overtone of the original pipe. Then, the fundamental frequency of the open pipe is

1. $200s^{-1}$

2. $100s^{-1}$

3. $250s^{-1}$

4. $300s^{-1}$

5. $150s^{-1}$

Q. A travelling pulse is given by y=4/(3x+48t+24xt+2) where x and y are in metre and t is in second. The velocity of wave pulse is?

Q.

A piston is fitted in a cylindrical tube of small cross section with the other end of the tube open. The tube resonates with a tuning fork of frequency 512 Hz. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of 32.0 cm. Calculate the speed of sound in the medium of the tube.

1. None of these

2. 

3. 

4. 

Q. The equations of two waves acting in perpendicular direction are given as $x=a\cos (\omega t+\delta )$ and $y=a\cos (\omega t+\alpha )$, where $\delta =\alpha +\frac{\pi }{2}$, the resultant wave represents

1. a parabola
2. a circle
3. an ellipse
4. a straight line

Q. A pulse or a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with

Q. The first overtone frequency of a closed organ pipe is equal to the second overtone frequency of an open organ pipe. If the length of the open pipe is $80\text{cm}$, what is the length of the closed organ pipe?

1. $20\text{cm}$
2. $40\text{cm}$
3. $60\text{cm}$
4. $80\text{cm}$

Q. A string vibrates in $5$ segments to a frequency of $480\text{Hz}$. The frequency that will cause it to vibrate in $2$ segments will be

1. $96\text{Hz}$
2. $192\text{Hz}$
3. $1200\text{Hz}$
4. $2400\text{Hz}$

Q. (a) Define a wavefront. Using Huygens' principle, verify the laws of reflection at a plane surface.
(b) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band ? Explain.
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the obstacle. Explain why ?

Q.

A uniform horizontal rod of length 40 cm and mass 1.2 kg is supported by two identical wires as shown in figure (15 - E9). Where should a mass of 4.8 kg be placed on the rod so that the same tuning fork may excite the wire on left into its fundamental vibrations and that on right into its first overtone ? Take $g=10m{s}^{-2}$

Q.

In an experiment with sonometer, a tuning fork of frequency $256Hz$ resonates with a length of $25cm$ and another tuning fork resonates with a length of $16cm$. The tension of the string remains constant. The frequency of the second tuning fork is

1. $163.84Hz$

2. $400Hz$

3. $320Hz$

4. $204.8Hz$

Q. A hollow metallic tube of length $L$ closed at one end produces resonance (in its fundamental mode) with a tuning fork of frequency $n$. The entire tube is then heated carefully, so that at equilibrium temperature, its length changes by $\ell$. If the change in velocity of sound is $v$, resonance (in fundamental mode) will now be produced by the tuning fork of frequency:
[Neglect end corrections]

1. $\frac{(V+v)}{\left[4\right(L+\ell \left)\right]}$
2. $\frac{(V+v)}{\left[4\right(L-\ell \left)\right]}$
3. $\frac{(V-v)}{\left[4\right(L+\ell \left)\right]}$
4. $\frac{(V-v)}{\left[4\right(L-\ell \left)\right]}$

Q.

Find the fundamental, first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is $340m{s}^{-1}$.

Q. A string of length $10\text{cm}$ fixed at one end and free at another end, has its fundamental frequency half that of second overtone for another string fixed at both ends. What will be the length of string fixed at both ends?
(Assume velocity of wave in both strings is same)

1. $20\text{cm}$
2. $40\text{cm}$
3. $10\text{cm}$
4. $30\text{cm}$

Q. A $1\text{m}$ long horizontal rope, having a mass of $40\text{g}$, is fixed at one end and is tied to a light string at the other end. The tension in the rope is $400\text{N}$. What will be the wavelengths (in $\text{metres}$) in the first and second overtone ?

1. $\frac{4}{3},\frac{4}{5}$
2. $\frac{5}{4},\frac{5}{3}$
3. $\frac{3}{4},\frac{3}{4}$
4. $\frac{4}{5},\frac{4}{3}$

Q. If fundamental frequency is $50\text{Hz}$ and next succesive frequencies are $150\text{Hz}$ and $250\text{Hz}$, then which of the following options correctly represents the state of the string?

1. String fixed at both end
2. String fixed at one end & free at other
3. String may be fixed at one end as well as at both ends
4. None of the above

Q. An open pipe vibrating in its fundamental frequency is suddenly closed at one end. As a result, the frequency of the third harmonic of the closed pipe is found to be higher by $100\text{Hz}$. The fundamental frequency of the open pipe is :-

1. $480\text{Hz}$
2. $200\text{Hz}$
3. $240\text{Hz}$
4. $30\text{Hz}$

Q. A standing wave is produced in a $10\text{m}$ long string fixed at one end and free at the other end. Find the wavelength of wave, if string is vibrating in its second overtone, and wave velocity is $20\text{m/s}$.

1. $4\text{m}$
2. $10\text{m}$
3. $5\text{m}$
4. $8\text{m}$

Q. Wavefronts incident on an interface between the media are shown in the figure. The refracted wavefronts will be as shown in

1. 
2. 
3. 
4. 

Q. A $12\text{cm}$ long vibrating string is fixed at one end and free at the other end. If the speed of wave on string is $48\text{cm/s}$ and string is vibrating in second overtone, find the frequency of vibration.

1. $5\text{Hz}$
2. $16\text{Hz}$
3. $2\text{Hz}$
4. $10\text{Hz}$

Q.

Spherical wave fronts shown in figure, strike a plane mirror. Reflected wave fronts will be as shown in

1. 

2. 

3. 

4. 

Q. Wave is travelling on a stretched string fixed at one end as shown in the figure. The resultant force acting on particle at point A is

1. Zero
2. In upward direction
3. In downward direction
4. Can't be determined

Q. Three aone dimensional mechanical waves in an elastic medium are given as $y1=2Asin(\omega t-kx),y2=2Asin(\omega -kx+\varphi )$
$y3=2Asin(\omega t+kx+\frac{\pi }{4})$ . For any value of $\varphi$ , the maximum displacement amplitude of the medium particles would be

1. $5A$
2. $3A$
3. $6A$
4. $4A$

Q.

It is desired to increase the fundamental resonance frequency in a tube which is closed at one end. This can be achieved by

1. Replacing the air in the tube by hydrogen gas

2. Increasing the length of the tube

3. Decreasing the length of the tube

4. Opening the closed end of the tube

Q. A certain string (fixed at one end and free at the other end) can vibrate at several frequencies, the lowest of which is $200\text{Hz}$. What are next two higher frequencies to which it vibrates?

1. $300\text{Hz},400\text{Hz}$
2. $600\text{Hz},1000\text{Hz}$
3. $200\text{Hz},250\text{Hz}$
4. $100\text{Hz},150\text{Hz}$