Class 11 Physics Waves: NCERT Solutions for Question 8

This page focuses on the detailed Waves question answers for Class 11 Physics Waves, addressing the question: 'A transverse harmonic wave on a string is described by y(x,t)  =  3.0 sin [36t + 0.018x + π /4] Where x and y are in cm and t in s. The positive direction of x is from left to right. (a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation? (b) What are its amplitude and frequency? (c) What is the initial phase at the origin? (d) What is the least distance between two successive crests in the wave?'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 8

A transverse harmonic wave on a string is described byy(x,t)  =  3.0 sin [36t + 0.018x + π /4]Where x and y are in cm and t in s. The positive direction of x is from left to right.(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?(b) What are its amplitude and frequency?(c) What is the initial phase at the origin?(d) What is the least distance between two successive crests in the wave?

(a) Yes; Speed = 20 m/s, Direction = Right to left

(b) 3 cm; 5.73 Hz

(c) π /4

(d) 3.49 m

Explanation:

Given,

y(x, t) =3 sin (36t +0.018x + π/4) . . . . . . . . . . . ( 1 )

( i ) We know, the equation of a progressive wave travelling from right to left is:

y (x, t) = a sin (ωt + kx + Φ) . . . . . . . . . . . . . . . . . . . ( 2 )

Comparing equation ( 1 ) to equation ( 2 ), we see that it represents a wave travelling from right to left and also we get:

a = 3 cm, ω = 36 rad/s , k = 0.018 cm and ϕ = π/4

( ii )Therefore the speed of propagation , v = ω/k = 36/ 0.018 = 20 m/s

( iii ) Amplitude of the wave, a = 3 cm

Frequency of the wave v = ω / 2π = 36 /2π = 5.7 hz

( iv ) Initial phase at the origin = π/4

( v ) the smallest distance between two adjacent crests in the wave, λ = 2π/ k = 2π / 0.018 = 349 cm