AP
Resonance tube experiment: measurement of velocity of sound
Resonance is the specific response of a system which is capable of vibrating with certain frequency to an external force acting with the same frequency.
The two conditions for occurring resonances are:
i) The frequency of applied force must be equal to the natural frequency of the system.
ii) The applied force must be in phase with the system.
In resonance tube experiment we mainly use two apparatus: tuning fork and resonance tube apparatus.
A tuning fork is a U shaped structure made up of steel or an alloy of the aluminum based on stem as shown in figure. The tuning fork is set in to vibration by striking into the rubber pad by holding the stem.
AP
Resonance tube apparatus consists of a glass tube G about a meter in length and 3-5 cm in diameter held vertically on a board as shown in figure. A meter scale is provided and is fitted on a board as in figure. The upper end of the tube is open and the lower end is connected to a reservoir which can slides up and down, thus changing the length of air column inside the glass tube.
Now a tuning fork of known frequency is set into vibration and held horizontally above the mouth of the tube. Ear is put near the open end of the tube, and a sound is heard. The length of air column in the tube is increased by lowering the reservoir. In doing so the condition is reached when the sound heard is maximum. This condition is known as first resonance and let it be l1, λ be the wavelength of sound and c be the end correction of the tube then,
l1 + c = λ/4 ……………………….(i)
Now if we go further increasing the length of air column inside the tube, the sound heard is at first decreasing and then minimum and then increasing and at certain point it becomes maximum again. This condition is called second resonance length and let it be l2then,
l2 + c = 3λ/4 ………………………(ii)
Subtracting (i) from (ii)
l2 –l1 = λ/2
Or, λ = 2(l2 –l1) ………………………….(iii)
If vt is the velocity of sound at t0C then, vt = λf
Where f is the frequency of the sound wave which is equal to the frequency of tuning fork.
Therefore, vt = 2f(l2 –l1) ……………………………….(iv)
Hence by determining the I and II resonance lengths and knowing the frequency of tuning fork, the velocity of sound in air at t0C can be determined.
The velocity of sound in air at 00C is,
……………….(v)
And at NTP is given by,
……………….. (vi)
Where P= atmospheric pressure, f=aqueous tension (SVP at room temperature and ϒ= coefficient of cubical expansivity of air.
1. What are beats? How are they formed?
2. Explain why we are unable to hear beats if the difference of frequency between two waves is greater than 10?
3. Define beat frequency and beat period?
4. What is organ pipe? How sound waves are produced in closed and open organ pipes?
5. What are the characteristics of vibration in closed and open organ pipes?
6. What do you mean by Rayleigh end correction in pipes?
7. Relate the fundamental note with harmonics and overtones in closed and open organ pipes?
8. Frequency of fundamental note of open organ pipe is double than that of closed organ pipe. Why?
9. How does frequency of open organ pipe varies with temperature. Explain why a pitch of an organ pipe is higher on a hot day?
10. Two organ pipes of same length but different diameters produce sound of different frequencies why?
11. Why is end correction necessary in pipes?
12. State the laws of transverse vibration of strings.
13. A guitarist tunes his guitar by tuning the tightening screws provided at the end .Explain how?
14. What is the effect of loading and filing the prongs of tuning fork?
15. Why resonance does not occur in the resonance tube exactly the three times of first resonating length?
16. What are harmonics and overtones?
17. Why are holes made in the wooden box of the sonometer? Explain.
18. A flute has several holes on it. Why?
19. How the fundamental frequency of sound in a closed organ pipe is affected if instead of air it is filled with a gas heavier than air?
20. Stringed instruments are provided with hollow boxes. Why?
21. How does frequency of sound changes when we go on filling an empty vessel?
22. What do you mean by resonance? Write the advantages and disadvantages of resonance?
23. The frequency of fundamental note of a closed organ pipe and that of open organ pipe are the same. What is the ratio of their length?
24. Why does empty vessel sound more than filled one?
25. Why is the tuning fork made up of two prongs? Would a tuning fork of any use if one of the prong is cut off?
26. When the tension on the string is increased by four times by what factor does the velocity of the wave in the string change?
27. What happens to the frequency of transverse vibration of a stretched string if its tension is halved and area of cross section of the string is doubled?
28. Explain with figure the formation of II overtone in a open pipe?
29. What do you mean by octave?
30. Why does a tuning fork sound louder when it is pressed against a table?
31. Why are rubbers used as vibration absorbers?
AP
Numerical Problem:
1. A tuning fork has frequency 440Hz. Another fork of slightly lower frequency is sounded together and 5 beats/sec is heard. What is the frequency of second tuning fork?
2. Two tuning forks when sounded together produces 5 beats per sec. The tuning fork A has frequency 480 Hz. The fork B is filed and the number of beats heard per sec. is 2. Determine the frequency of tuning fork B before and after filing? 475Hz, 478Hz
3. Two tuning forks A and B produce 10 beats/sec when sounded together. On loading the fork A slightly, it was observed that 15 beats are observed in one second. If the frequency of the fork B is 480Hz, calculate the frequency of fork A a) before and b) after loading? 470HZ, 465Hz
4. A note produces 4 beats/sec with a tuning fork of frequency 512Hz and 6 beats/sec with a tuning fork of frequency 514 Hz. Find the frequency of a note? 508Hz
5. In a resonance tube expt., the first and second resonance lengths are observed at 17cm and 52.6cm respectively. The tuning fork used was of frequency 512 Hz and the temp was 270C. Calculate the velocity of sound in air at 00C and the end correction of the tube?347.7m/s, 0.8cm
6. An open pipe 30cm long and a closed pipe 23 cm long, both of the same diameter, each sounds their first overtone. If they are in resonance find the end correction of these pipes? 1cm
7. A uniform tube 60cm long stands vertically with its lower end dipping into water. When the length above the water is 14.8cm and again when it is 48cm, the tube resounds to a vibrating tuning fork of frequency 512 Hz. Find the lowest frequency to which the tube will resound when it is open at both ends. 267Hz
8. An organ pipe is tuned to a frequency of 440Hz when the temperature is 270C. Find its frequency when the temperature drops to 00C. Assume both ends of pipe open. 419.7Hz
9. The length of an organ pipe is 30cm. what is the change in its length required to maintain its frequency unchanged if the temperature falls from 270C to 70C? 1.02cm
10. An open pipe 32cm long and closed pipe 24 cm long, both of the same diameter are each sounding its first overtone and these are in unison. What is the end correction of these pipes? 0cm
11. Two organ pipes gives 4 beats per second when sounded together at 50C. Calculate the number of beats at 350C? 4.2
12. Two sound waves of wavelengths 50cm and 50.4cm produce 6 beats per second in the gaseous medium. Calculate the velocity of sound in gas? 378m/s
13. A certain closed organ pipe resonates with a frequency of 440 Hz in air. If the pipe is filled with CO2 at the same temperature, at what frequency does it resonate? Take velocity of sound in air = 350m/s, density of CO2= 1.997 Kg/m3 and density of air = 1.293kgm-3. 354Hz
14. Find the fundamental frequency and first four overtone for a 15.00cm long pipe which is (a) open at both ends, (b) closed at one ends. How many overtones a person having normal hearing distinguish in each case. Vsound = 344 m/s. 16,17
15. A steel wire is 2m and whose mass is 3g is under tension of 500N and is tied down at both ends. Calculate the frequency and wavelength for fundamental modes. 144.25Hz, 4m
16. A wire of diameter 0.04cm and made of steel of density 8000 kgm-3 is under a constant tension of 80N. What length of this wire should be plucked to cause it to vibrate with a frequency of 840 Hz? 0.168m
17. A piano string has a length of 2m and a density 8000 Kgm-3. When the tension in string produces a strain of 1%, the fundamental note obtained from the string in transverse vibration is 170Hz. Calculate the value of Young’s modulus value for the material of the string? 3.7x1010N/m2
18. A piano string 1.5m long is made of steel of density 7800 Kgm-3 and Young’s modulus 2x1011Nm-2 It is maintained at a tension which produces an elastic strain of 1% in the string. Find frequency of transverse vibration of string when it is vibrating in second mode of vibration? 168.8Hz
19. Find the ratio of length of closed pipe to that of an open pipe in order that the second overtone of the former is in unison with the fourth overtone of the latter? 1:2
20. Two closed organ pipe give eight beats per second when sounded together at 00C. Calculate the number of beats heard per second at 270C? 8.4
21. A metal wire is stretched by a weight of 13.5Kg between rigid supports 0.5m apart. The diameter of the wire is 0.35mm and the density of the metal is 8800 Kgm-3. What is the fundamental frequency of the note emitted by the wire when it vibrates transversely? 396.86Hz
22. A string when stretched by a weight of 4 kg gives a note of frequency 256Hz. What weight will produce octave of this note? 16Kg
23. A sonometer wire is stretched by hanging a metal cylinder of density 8000Kgm-3at the end of the wire. A fundamental note of 256Hz is sounded when the wire is plucked. Calculate the frequency of vibration of the same length of the wire when a vessel of water is placed so that the cylinder is totally immersed. 239.5Hz
24. What is the percentage change in frequency of fundamental note produced by a guitar string when the string diameter 0.93m is used instead of 0.90m? 3.2%
25. Two identical steel wires have fundamental frequencies of vibrations 400 cycles per second. The tension in one of the wire is increased by 2% and both wires are plucked. How many beats occurred per second? beats/s
26. A tuning fork of unknown frequency is in unison with 20cm of a stretched wire. Keeping the tension constant, if the length of wire is (a) increased and (b) decreased by 2mm, 4 beats are heard. What is the frequency of unknown fork? 400Hz
27. A stretched wire gives 2 beats/s with a tuning fork when its length is 1.43m and also when its length is 1.45m, the tension being the same in each case. What is the frequency of tuning fork?
28. The length of sonometer wire between two fixed ends is 100cms. Where two bridges should be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1:2:3? 54.55cm &81.82 cm
29. A steel wire of length 40.0cm and diameter 0.0250cm vibrates transversely in unison with a tube, open at each end and the effective length 60.0 cm, when each is sounding its fundamental note. The air temperature is 270C. Find the tension in the wire? (assume the velocity of sound in air at 00C is 331ms-1 and the density of steel is 7800Kgm-3) 20.5N
30. A steel wire of length 100cm and density 8gm/cm3 is stretched tightly between two rigid supports. It is vibrating in its fundamental mode with frequency 200Hz. (a) what is the speed of transverse wave in this wire? (b) what is the longitudinal stess in this wire? (c) if the maximum acceleration at the midpoint of the wire is 800ms-2, what is the amplitude of vibration at the midpoint? 400m/s, 1.28x109Nm-2, 0.5 mm