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Waves physics ncert solutions class 11th Physics Class 11th Physics Waves

15.9 For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase ?

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Vishal Baghel | Contributor-Level 10

5 months ago

All the waves have different phases. The given transverse harmonic wave is:

y(x, t) = 3.0 sin (36t + 0.018x + $\frac{π}{4}$ ) ………(i)

For x = 0, the equation reduces to

y (0,t) = 3.0 sin (36t + $\frac{π}{4}$ )

Also $ω$ = $\frac{2 π}{T}$ , so T = $\frac{2 π}{ω}$ = $\frac{2 π}{36}$ = $\frac{π}{18}$ s

For plotting y vs., t graphs using different values of t, we get

When t = 0, y = 2.12

t = $\frac{T}{8}$ = $\frac{π}{18 \times 8}$ , y = 3

t = $\frac{2 T}{8}$ = $\frac{2 \times π}{18 \times 8}$ , y = 2.12

t = $\frac{3 T}{8}$ = $\frac{3 \times π}{18 \times 8}$ , y = 0

t = $\frac{4 T}{8}$ = $\frac{4 \times π}{18 \times 8}$ , y = -2.12

t = $\frac{5 T}{8}$ = $\frac{5 \times π}{18 \times 8}$ , y = -3

t = $\frac{6 T}{8}$ = $\frac{6 \times π}{18 \times 8}$ , y = -2.12

t = $\frac{7 T}{8}$ = $\frac{7 \times π}{18 \times 8}$ , y = 0

For x

...more

All the waves have different phases. The given transverse harmonic wave is:

y(x, t) = 3.0 sin (36t + 0.018x + $\frac{π}{4}$ ) ………(i)

For x = 0, the equation reduces to

y (0,t) = 3.0 sin (36t + $\frac{π}{4}$ )

Also $ω$ = $\frac{2 π}{T}$ , so T = $\frac{2 π}{ω}$ = $\frac{2 π}{36}$ = $\frac{π}{18}$ s

For plotting y vs., t graphs using different values of t, we get

When t = 0, y = 2.12

t = $\frac{T}{8}$ = $\frac{π}{18 \times 8}$ , y = 3

t = $\frac{2 T}{8}$ = $\frac{2 \times π}{18 \times 8}$ , y = 2.12

t = $\frac{3 T}{8}$ = $\frac{3 \times π}{18 \times 8}$ , y = 0

t = $\frac{4 T}{8}$ = $\frac{4 \times π}{18 \times 8}$ , y = -2.12

t = $\frac{5 T}{8}$ = $\frac{5 \times π}{18 \times 8}$ , y = -3

t = $\frac{6 T}{8}$ = $\frac{6 \times π}{18 \times 8}$ , y = -2.12

t = $\frac{7 T}{8}$ = $\frac{7 \times π}{18 \times 8}$ , y = 0

For x = 2 and x = 4. The phases of the three waves will get changed, frequency and amplitude will remain unchanged for any change of x.

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15.9 For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase ?

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