Q30 of 36 Page 110

A tuning fork vibrating with a frequency of 512Hz is kept close to the open end of a tube filled with water (Fig. 15.4). The water level in the tube is gradually lowered. When the water level is 17cm below the open end, maximum intensity of sound is heard. If the room temperature is 20° C, calculate

(a) speed of sound in air at room temperature


(b) speed of sound in air at 0° C


(c) if the water in the tube is replaced with mercury, will there be any difference in your observations?



Given:


Frequency of tuning fork = 512 Hz


Water level below open end = 17 cm


The water acts as a reflective surface for the wave, therefore the tube behaves like an organ pipe. When the water level is such that the frequency of the wave matches the resonant frequency of the organ pipe the maximum sound is heard.


(a) Since at 17 cm maximum intensity of sound is heard, it corresponds to amplitude of the wave. For the first harmonic the length of the organ pipe equals one-fourth the wavelength of the wave. Hence,



Where, l is the length of the pipe and λ is the wavelength



Now velocity of wave



where f is the frequency of the wave.



(b) We know that velocity of air is given by



where γ is the ratio of specific heat at constant pressure to specific heat at constant volume for air, R is the universal gas constant, T is temperature and M is the mass of the gas. Keeping everything constant except temperature,



Let the velocity of sound in air at 0° C be v0 and the velocity at temperature 20° be v20, then






(c) When water is replaced with mercury all the observations will remain same, however mercury is more reflective than water and therefore the intensity of the sound heard will be increased.


More from this chapter

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28

The wave pattern on a stretched string is shown in Fig. 15.2. Interpret what kind of wave this is and find its wavelength.


 29

The pattern of standing waves formed on a stretched string at two instants of time are shown in Fig. 15.3. The velocity of two waves superimposing to form stationary waves is 360 ms-1 and their frequencies are 256 Hz.


(a) Calculate the time at which the second curve is plotted.


(b) Mark nodes and antinodes on the curve.


(c) Calculate the distance between A′ and C′.


 31

Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.

 32

The earth has a radius of 6400 km. The inner core of 1000 km radius is solid. Outside it, there is a region from 1000 km to a radius of 3500 km which is in molten state. Then again from 3500 km to 6400 km the earth is solid. Only longitudinal (P) waves can travel inside a liquid. Assume that the P wave has a speed of 8 km s-1 in solid parts and of 5 km s-1 in liquid parts of the earth. An earthquake occurs at some place close to the surface of the earth. Calculate the time after which it will be recorded in a seismometer at a diametrically opposite point on the earth if wave travels along diameter?