A transverse wave on a string is described by y=3 (36t+0.018x+ /4 ), where x, y are in cm and t in seconds. The least distance between the two successive crests in the wave is cm. (Nearest integer) ( =3.14)
349
Comparing with y=A ( t+kx+ ): k=0.018 cm-1
Distance between two successive crests = = 2 k
⇒ = 2 3.140.018 cm=348.9 cm
∴ 349 cm
Answer: 349
The equation of a plane progressive wave is given by y=5 (200t- x150 ) where x and y are in cm and t is in second. The velocity of the wave is m/s.
The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to m/s.
Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is Hz.
The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is
The velocity of sound in air is doubled when the temperature is raised from 0 to . The value of is .
Two loudspeakers (L1 and L2) are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point A, equidistant from both loudspeakers, is moved by 25 m along the line AB while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is Hz (Speed of sound in air is 324 m/s and 5 = 2.23) [figure]
In an open organ pipe 3 and 6 are 3rd and 6th harmonic frequencies, respectively. If 6 - 3 = 2200 Hz then length of the pipe is mm. (Take velocity of sound in air is 330 m/s.)
Two strings (A, B) having linear densities A = 2 10-4 kg/m and B = 4 10-4 kg/m and lengths LA = 2.5 m and LB = 1.5 m respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time t1 and t2, respectively, to reach the joint. The ratio t1/t2 is:
The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y1(x, t) = 4 (kx - t) and y2(x, t) = 2 (kx - t + 2 3 ), are: (Take the angular frequency of initial waves same as )
Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is v1, and that in the other string having radius of cross section R/2 is v2. Then v2v1 =