Waves

This is a multiple choice answer as classified in NCERT Exemplar

(a, b, d) As we know by y (x, t) = 0.06 sin (2πx/3) cos (120πt)

By comparing the equation with general equation N denotes nodes and A denotes antinodes.

(a) Clearly frequency is common for all the points

(b) Consider all the particles between two nodes they are having same phase at given time

(c) But are having different amplitude of 0.06sin (2 $\frac{\pi }{3}x$ ) and because of different amplitudes they are having different energies.

This is a multiple choice answer as classified in NCERT Exemplar

(b, c, d)

during propagation of a plane progressive mechanical wave

(i) clearly the particles O, A and B are having different phase.

(ii) Particles of the wave are having up and SHM.

(iii) For a progressive wave propagating in a fluid

V= $\sqrt[]{\frac{B}{\rho }}$ , V= $\sqrt[]{\frac{1}{\rho }}$

This is a multiple choice answer as classified in NCERT Exemplar

(c, d) Speed of sound waves in a fluid is given by

V= $\sqrt[]{\frac{B}{\rho }}$

V= $\frac{1}{\sqrt[]{\rho }},$ V $\propto \sqrt[]{B}$ so when we increase velocity bulk modulus also increases.

This is a multiple choice answer as classified in NCERT Exemplar

(b, c) y (x, t) = 0.06 sin (2πx/3) cos (120πt)

(a) y (x, t)=asinkxcoswt

(b) w=120 $\pi$ , f=60hz

(c) k=2 $\frac{\pi }{3}=\frac{2\pi }{\lambda },\lambda =3m,f=60hz$ , v =60 (3)=180m/s

(d) since in stationary wave all particles of the medium executes SHM with varying amplitude nodes.

This is a multiple choice answer as classified in NCERT Exemplar

(a, b, c) y (x, t)=30sin (36t+0.018x+ $\frac{\pi }{4}$ )

Y=asin (wt+kx+ $\varnothing$ )

(a) as the equation involves positive sign with x . hence the wave is travelling from right to left. Hence option a is correct.

(b) W=36

2 $\pi v=36$

$v=\frac{36}{2\pi }$ = $\frac{18}{\pi }$

$k=0.018=\frac{2\pi }{\lambda }$

$\frac{2\pi v}{v\lambda }=0.018$

w/v=0.018

v=2000cm/s=20m/s

(c) 2 $\pi v=36$

$v=\frac{18}{\pi }$ = 5.7Hz

(d) $\frac{2\pi }{\lambda }=0.018$ , $\lambda =2\pi$ /0.0018cm=3.48cm

This is a multiple choice answer as classified in NCERT Exemplar

(c) Let frequency of the source is n_o

Let the speed of sound wave in the medium is v

As observer is stationary

Apparent frequency n_a= $\frac{v}{v-v_s}{n}_o$

$\frac{v}{v-v_s}{n}_o=n_a{n}_o$

When the train is going away from the observer

Apparent frequency n_a= $\frac{v}{v-v_s}{n}_o$ = $n_a<n_o$

This is a multiple choice answer as classified in NCERT Exemplar

(b) m=2.5kg

$\mu =$ mass per unit length

=m/l =2.5/20=125/10=0.125kg/m

V= $\sqrt[]{\frac{T}{\mu }}=\sqrt[]{\frac{200}{0.125}}$

L=v $*t$

20= $\sqrt[]{\frac{125}{2*{10}^5}}=20*\sqrt[]{\frac{25*5}{2*{10}^5}}$

= 20 $*\sqrt[]{\frac{25}{0.4*{10}^5}}=\frac{1}{2}$

This is a multiple choice answer as classified in NCERT Exemplar

(b) Amplitude of reflected wave

A_f= $\frac{2}{3}*A_i$ =2 (0.6)/3=0.4 units

Equation of incident wave

Y_i=0.6sin2 $\pi \left(t-\frac{x}{2}\right)$

For reflected wave 

y_r=A_rsin2 $\pi$ (t+x/2+ $\pi$ )

Y_r=-0.4sin2 $\pi \left(t+\frac{x}{2}\right)$

This is a multiple choice answer as classified in NCERT Exemplar

(d) Due to compression and rarefactions density of the medium changes.at compressed regions density is maximum and at rarefactions density is minimum

As density is changing so boyle, s law not obeyed

Bulk modulus remains same

The time of compression and rarefaction is too small so no transfer of heat.

This is a multiple choice answer as classified in NCERT Exemplar

(c) When mechanical transverse wave propagates through a medium, the constituents of the medium oscillate perpendicular to wave motion causing change in shape. That is each element of the medium is subjected to shearing stress. Solids and strings have shear, that is why tey bear stress. But in fluids there is no fixed shape so transverse waves does not formed in fluid.