Q: The displacement y of a particle in a medium can be expressed as, y=10^ -6 (100 t+20 x+ 4 ) m where t is in second and x in meter. The speed of the wave is

From equation given, array l =100 \\ and k =20 \\ v = k = 100 20 =5 ~m / s array

Question 1

The speed of sound in oxygen at S.T.P. will be approximately: (Given, . R =8.3 JK ^ -1 , =1.4 )

Accepted Answer

At STP Temperature, T=273 ~K Molecular mass of oxygen, M =32 10^ -3 ~kg Speed of sound is given by v = RT M = 1.4 8.3 273 32 10^ -3 =314.8541 315 ~m / s

Question 2

A plane progressive wave is given by y=2 2 (330 t-x) m . The frequency of the wave is:

Accepted Answer

Equation of wave is, y=2 2 (330 t-x) m y=A ( t-k x) On comparing =2 330 2 f =2 330 f =330 ~Hz [ =2 ~F ]

Question 3

The engine of a train moving with speed 10 ~ms ^ -1 towards a platform sounds a whistle at frequency 400 ~Hz . The frequency heard by a passenger inside the train is (neglect air speed. Speed of sound

Accepted Answer

The relative velocity of a passenger with respect to source of sound (engine of train) is 0 . So there will be no Doppler's effect. So frequency heard is 400 ~Hz .

Question 4

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

Accepted Answer

Given M _ H _2 =2 ; M _ O _2 =32 Speed of sound, v = RT M v 1 M v _ H _2 v _ O _2 = M _ O _2 M _ H _2 = 32 2 =4: 1

Question 5

A submarine A travelling at 17 ~m / s is being chased along the line of its velocity by another submarine B travelling at 34 ~m / s . B sends a sonar signal of 600 ~Hz to detect A and receives a refle

Accepted Answer

Given, velocity of submarine A, v_A=17 ~m / s Velocity of submarine B, v_B=34 ~m / s Signal sent by submarine B is detected by submarine A can be shown as Freqency of the signal, f_0=600 ~Hz Speed of sound in water v_s=1500 ~ms ^ -1 Frequency received by submarine A is f_1= ( v_ S -v_A v_ S -v_B ) f_0= [ 1500-17 1500-34 ] 600 ~Hz f_1= 1483 1466 600 Frequency received by submarine B is f_2= ( v_ S +v_B v_s+v_A ) f_1 Substituting given values and f_1 value from Eq. (i), we get aligned f_2 & = ( 15

Question 6

Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of the waves i

Accepted Answer

The velocity of transverse waves is given by v= T m where, T= Tension and m= mass per unit length of the wire. If r is the radius of the wire and its density then, m= r^2 v= T m = T r^2 v_A= T_A r_A and v_B= T_B r_B Now, v_A v_B = T_A T_B r_B r_A r_A=2 r_B and T_A= 1 2 T_B Hence, v_A v_B = 1 2 2

Question 7

A direct current of 6 ~A is superimposed on an alternating current I=10 t flowing through a wire. The effective value of the resulting current will be

Accepted Answer

Given, I=6+10 t aligned I_ eft & = [ . _0^T I^2 d t ]^ 1 / 2 _0^T d t = [ 1 T _0^T(6+10 t)^2 d t ]^ 1 / 2 . \ & = [ 1 T _0^T (36+120 t+100 ^2 t ) d t ]^ 1 / 2 aligned But as, 1 T _0^T t d t=0 and 1 T _0^T ^2 t= 1 2 I_ eff = [36+ 1 2 100 ]^ 1 / 2 =9.27 Thus, I_ eff =9.27 ~A .

Question 8

The frequency of whistle of an engine appears to be (4 / 5)^ th of initial frequency when it crosses a stationary observer. If the velocity of sound is 330 ~m / s , then the speed of engine will be

Accepted Answer

n^ = n v v-v_ s (1) n^ = n v v+v_ s . .(2) From (1) and (2), n^ n^ = v+v_ s v-v_ s . .(3) According to question, n^ n^ = 5 4 v_ s =? v=330 ~m / s .(4) From eq. (3) and (4) 5 4 = [ 330+v_ s 330-v_ s ] 9 v_ s =330 v_ s =36.6 ~m / s

Question 9

The displacement y of a particle in a medium can be expressed as, y=10^ -6 (100 t+20 x+ 4 ) m where t is in second and x in meter. The speed of the wave is

Accepted Answer

From equation given, array l =100 \ and k =20 \ v = k = 100 20 =5 ~m / s array

Waves and Sound — Previous Year Questions & Solutions