SATHEE: Waves - Result Question 18

Waves - Result Question 18

18. The equation of a travelling wave is

$y = 60 \cos (180 t - 6 x)$

where $y$ is in microns, $t$ in second and $x$ in metres. The ratio of maximum particle velocity

to velocity of wave propagation is [1997]

(a) 3.6

(b) $3.6 \times 10^{- 4}$

(d) $3.6 \times 10^{- 11}$

Show Answer

Answer:

Correct Answer: 18. (b)

Solution:

(b) $y = 60 \cos (180 t - 6 x)$ $ω = 180, k = 6 \Rightarrow \frac{2 π}{λ} = 6$

Wave velocity,

$v = \frac{ω}{k} = \frac{2 π}{T} \times \frac{λ}{2 π} = \frac{180}{6} = 30 m / s$

Differentiating (1) w.r.t. $t$ ,

Particle velocity,

$v_{p} = \frac{d y}{d t} = - 60 \times 180 \sin (180 t - 6 x)$

$v_{p max} = 60 \times 180 μ m / s$

$= 10800 μ m / s = 0.0108 m / s$

$\frac{v_{p max}}{v} = \frac{0.0108}{30} = 3.6 \times 10^{- 4}$

Wave velocity $(v)$ is the distance travelled by the disturbance in one second. It only depends on the properties of the medium and is independent of time and position.

$V = n λ = \frac{λ}{T} = \frac{ω λ}{2 π} = \frac{ω}{k}$

Waves - Result Question 18

18. The equation of a travelling wave is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Waves - Result Question 18

18. The equation of a travelling wave is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu