Q29 of 36 Page 110

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′.


Given:


Frequency of the wave = 256 Hz


Velocity of the wave = 360ms-1


(a) In the second instant, all the points of the wave are at the mean position. The time taken to reach the mean position from the amplitude is therefore the time at which the second curve is plotted. The distance to reach the mean position from the amplitude is distance between a node and an antinode that equals one-fourth the wavelength. The wavelength therefore is given by,



where v is the velocity and f is the frequency of the wave.



And



Therefore time taken to reach mean position,



Therefore, the second curve was plotted at time of t = 9.72 x 10-4 s.


(b) Nodes are points that undergo the minimum displacement and antinodes are points that undergo the maximum displacement. Thus, the points A, B, C, D, E, are the node and the points A’ and C’ are the antinodes.


(c) A’ and C’ are successive antinodes, and the distance between two successive antinodes is the wavelength of the wave, therefore



More from this chapter

All 36 →
27

A train standing at the outer signal of a railway station blows a whistle of frequency 400 Hz still air. The train begins to move with a speed of 10 m s-1 towards the platform. What is the frequency of the sound for an observer standing on the platform? (sound velocity in air = 330 m s-1)

 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.


 30

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?



 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.