The phenomenon of beats can take place
A. for longitudinal waves only

B. for transverse waves only

C. for both longitudinal and transverse waves

D. for sound waves only

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.

A 200 m-long rope, having a mass of 80 g, is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N. (A) Find the frequencies of the fundamental and the first two overtones. (B) Find the wavelength in the fundamental and the first two overtones.

Figure (15-E11) shows a string stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a particular tuning fork. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the density of the material of the block.

A string of length L fixed at both ends vibrates in its fundamental mode at a frequency v and a maximum amplitude A. (A) Find the wavelength and the wave number k. (B) Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along The direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.

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?

A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of 1237.5 Hz? (sound velocity in air = 330 m s^-1)

A 40 cm wire having a mass of 32 g is stretched between two fixed supports 4005 cm apart. In its fundamental mode, the wire vibrates at 220 Hz. If the area of cross section of the wire is 10 mm², find its Young modulus.

A uniform horizontal rod of length 40 cm and mass 12 kg is supported by two identical wires as shown in figure (15-E9). Where should a mass of 48 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 = 10 m s⁻¹.

A particular guitar wire is 300 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes?

A string of linear mass density 05 g cm⁻¹ and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end (figure 15-E4). The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cm s⁻¹. The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. (A) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape. (B) The shape of the string changes periodically with time. Find this time period. (C) What is the tension in the string?