Question 1

For a travelling harmonic wave y(x, t) = 2.0\ \ 2 (10\ t - 0.0080\ x + 0.35), where x and y are in cm and t in s. The phase difference between oscillatory motion of two points separated by a distance

Accepted Answer

The given equation of the travelling harmonic wave is y(x, t) = 2.0 2 (10 t - 0.0080 x + 0.35). Comparing this with the standard wave equation y(x, t) = A ( t - kx + _0), we get the wave number k = 2 0.0080 rad/cm. The distance between the two points is given as x = 0.5 m = 50 cm. The phase difference between two points separated by a distance x is given by = k x. Substituting the values, we get: = (2 0.0080) 50 = 2 0.4 = 0.8 rad. Answer: 0.8\ rad

Question 2

For sound waves, if the number of nodes for the 5^ th harmonic of an open-ended pipe is n and that for the 9^ th harmonic of the same pipe with one of its ends closed is m, the ratio n m is :

Accepted Answer

For an open-ended pipe, the p^ th harmonic contains p nodes and p+1 antinodes. For the 5^ th harmonic of the open-ended pipe, the number of nodes is n = 5. For a pipe closed at one end, only odd harmonics are present. The q^ th harmonic (where q is an odd integer) contains q+1 2 nodes and q+1 2 antinodes. For the 9^ th harmonic of the closed pipe, the number of nodes is m = 9+1 2 = 5. The ratio of the number of nodes is n m = 5 5 = 1.

Question 3

A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to :

Accepted Answer

For open pipe f = V 2 When half of its length is dipped in water, Now it is COP. aligned & f ^ = V 4( / 2) \ & f ^ = V 2 \ & f ^ = f aligned

Question 4

The displacement of a travelling wave y=C 2 (at -x ) where t is time, x is distance and is the wavelength, all in S.I. units. Then the frequency of the wave is

Accepted Answer

y=c 2 ( at -x) y=c ( 2 . at .- 2 x ) Comparing with y=A ( -k x) =2 f= 2 a f= a

Waves and Sound — Previous Year Questions & Solutions