THEORETICAL QUESTIONS

  1. [2082] The given figure shows standing wave formed in an open organ pipe.
  1. Which mode of vibration is shown?  [1]
  2. Obtain the frequency of vibration for this mode.  [1]
  1. [2081 GIE ‘A’] Discuss the different modes of vibration of an air column in an open organ pipe.  [3]
  2. [2081 GIE ‘B’] Describe the various modes of vibration of air column in a closed organ pipe.  [3]
  3. [2081 GIE ‘B’] How stationary waves are formed in an open organ pipe?  [1]
  4. [2081 ‘B/C’] The diagram shows a standing wave in an open organ pipe.
  1. Redraw the diagram and show the position of nodes and antinodes.  [1]
  2. Derive an expression for frequency of this mode.  [2]
  1. [2081 ‘B/C’] What will be the effect of velocity of transverse wave in a stretched string if the radius of the string is doubled?  [2]
  2. [2081 ‘D’] Given figure represents the sonometer wire under certain tension T.
  1. Does the frequency of fundamental vibration of wire depend on the value of hanging weight? Justify.  [1]
  2. What will be the value of fundamental frequency of vibration of the wire if the hanging weight is immersed in a liquid of upthrust U?  [1]
  3. Describe the different modes of vibration in a closed organ pipe.  [3]
  1. [2080 GIE ‘A’]
  1. Define an open organ pipe.  [1]
  2. Describe various modes of vibration air column in an open organ pipe.  [3]
  1. [2080 GIE ‘A’] A musician tunes his guitar by turning the screws provided at the end, why?  [2]
  2. [2080 GIE ‘B’] What do you mean by harmonics and overtones?  [2]
  3. [2080 ‘P’] Define an organ pipe.  [1]
  4. [2080 ‘R’] The given figure shows the first overtone of a stretched string of length L.


i. Define harmonics and overtones.  [1]
ii. Calculate the frequency of this mode.  [2]
iii. If the tension of the string is increased 4 times, what will be the frequency of this mode?  [2]

13. [2079 GIE ‘B’]
a. What are organ pipes?  [1]
b. Describe first and second modes of vibration of air column inside a closed organ pipe.  [2]

14. [2079 ‘O’]
a. Define an organ pipe.  [1]
b. Describe the various modes of vibration of the air column in a closed organ pipe.  [3]
c. What is end correction?  [1]

15. [2079 ‘V’]
a. What are stationary waves?  [1]
b. How stationary waves are formed in an open organ pipe?  [1]
c. Sketch the wave pattern and calculate the frequencies of fundamental vibration and the first overtone for the open organ pipe of length ‘L’.  [3]

Old Course

SHORT ANSWER QUESTION

16. [2074 ‘B’] The frequency of a fundamental note of a closed organ pipe and that of an open organ pipe are the same. What is the ratio of their lengths?

17. [2073 ‘C’, 2073 ‘D’] By what factor does the velocity of transverse wave in the string change when the tension in the stretched string is increased by four times.

18. [2072 ‘S’] The six strings of a guitar are of same length and are under nearly the same tension, but have different thickness. On which string do waves travel the fastest?

19. [2072 ‘S’] How does the pitch of an organ pipe change with temperature?

20. [2072 ‘E’] A tuning fork has two prongs. Why?

LONG ANSWER QUESTION

1. [2078 ‘C’] What is resonance? Describe an experiment to determine the velocity of sound in air and end correction of the tube by resonance method.

2. [2077 ‘D’] Prove, with necessary diagrams, that both types of harmonics odd and even can be obtained in an organ pipe open at both ends. What is end correction of a pipe?

3. [2076 GIE ‘A’] What is meant by end correction? Discuss the vibration of air column of open pipe and show that both harmonics are produced on it.

4. [2076 ‘C’, 2074 ‘S’] Define end correction. Show that both harmonics, odd and even, can be produced in an open pipe open at both ends.

5. [2075 ‘S’] State the laws of transverse vibration in a stretched string. Describe various modes of vibration in a stretched string.

6. [2075 ‘A’] What do you understand by “harmonics” and “overtone” in the case of organ pipe? Also prove that only odd harmonics are produced in closed ended organ pipe.

OR [2072 ‘D’] What is end correction of a pipe? Describe the different modes of vibration of air column in an organ pipe closed at one end.

7. [2075 ‘B’] What are harmonics? Explain the formation of overtones in an open and a closed organ pipe.

8. [2074 ‘A’] Describe an experiment with the necessary theory by which the speed of sound in air is determined by using resonance tube method.

9. [2073 ‘D’] What is the difference between an open and a closed pipe? Explain with proper sketches for the formation of second overtones in each case. Also express the length of pipes in terms of the wavelength of sound.

NUMERICAL PROBLEMS

New Course

1. [2082] Guitar string of length 1.5 m is made of steel of density [latex]7800 \text{kg/m}^3[/latex] and Young’s modulus [latex]2\times 10^{11} N/m^2[/latex]. It produces an elastic strain of 1% in the string. Calculate:  [3]

i. stress developed in the string.

ii. frequency of second mode of vibration.

Ans: [latex]2\times 10^9 N/m^2[/latex], [latex], 337 \text{Hz}[/latex]

2. [2081 GIE ‘A’] A sonometer wire of density [latex]9\ \text{gm/cm}^3[/latex] and length 1 m is subjected to an extension of 0.05 cm. What is the lowest frequency of transverse vibration in the wire? Assume Young’s modulus [latex]Y = 9\times 10^{10} Nm^{-2}[/latex].  [2]

Ans: [latex]35.36\ \text{Hz}[/latex]

3. [2080 GIE A] A steel wire of length 1 m long has a mass of 80 gm and is stretched with a tension of 1000 N. Calculate the fundamental frequency of transverse vibration.  [2]

Ans: [latex]112\ \text{Hz}[/latex]

4. [2080 GIE B] In a resonance tube experiment, the first and second resonance positions were observed at 17 cm and 52.6 cm respectively. The frequency of tuning fork used was [latex]512 \text{Hz}[/latex] and the room temperature was [latex]27^\circ C[/latex]. Calculate the velocity of sound in air at room temperature and end correction of the pipe. What would be the velocity of sound in air if the temperature drops to [latex]0^\circ C[/latex]?  [3]

Ans: [latex]364.5 \text{m/s}, 347.75 ,\text{m/s}, 0.008 \text{m}[/latex]

5. [2080 P] What is the ratio of length of two pipes, an open organ pipe A and a closed organ pipe B both vibrating in third overtones are in resonance? Justify.  [2]

Ans: [latex]\frac{8}{7}[/latex]

6. [2079 GIE B] An organ pipe open at both ends is 0.5 m long. What is the fundamental frequency if velocity of sound is [latex]350 ,\text{m/s}[/latex]?  [2]

Ans: [latex]350 \text{Hz}[/latex]

Old Course

7. [2076 GIE B] One day when speed of sound is [latex]340 ,\text{m/s}[/latex], the fundamental frequency of a closed organ pipe is [latex]220 \text{Hz}[/latex] (a) How long is this pipe? (b) The second overtone of this pipe has the same wavelength as third harmonic of an open pipe. How long is the open pipe?

Ans: [latex]0.386 \text{m}, 0.31 \text{m}[/latex]

8. [2076 ‘B’/2073 ‘B’] A wire whose mass per unit length is [latex]10^{-3} \text{kg/m}[/latex] is stretched by a load of 4 kg over the two bridges of a sonometer wire 1 m apart. It is struck at its middle point, what would be the wavelength and frequency of its fundamental vibration?

Ans: [latex]2 \text{m}, f = 100 \text{Hz}[/latex]

9. [2074 ‘B’] A steel wire of length 20 cm and mass 5 gram is under the tension of 500 N and is tied down at both ends. Calculate the frequency of fundamental mode of vibration.

Ans: [latex]353.5 \text{Hz}[/latex]

10. [2073 ‘S’] A pianofort wire having a diameter of 0.90 mm is replaced by another wire of the same material but with diameter 0.93 mm. If the tension of the wire is as before. What is percentage change in the frequency of fundamental note?

Ans: [latex] 3.2 %[/latex]

11. [2072 ‘S’] On a day when the speed of sound is [latex]345 \text{m/s}[/latex], the fundamental frequency of a closed organ pipe is [latex]220 \text{Hz}[/latex]. The second overtone of this pipe has the same wavelength as the third harmonic of an open pipe. How long is the open pipe?

Ans: [latex]47 \text{cm}[/latex]

12. [2072 ‘C’] A wire with mass 40 g is stretched so that its ends are tied down at points 80 cm apart. The wire vibrates in its fundamental mode with frequency [latex]60 \text{Hz}[/latex]. Calculate the speed of propagation of transverse waves in the wire and the tension in the wire.

Ans: [latex]v = 96 \text{m/s}, T = 460.8 \text{N}[/latex]

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