The displacement of a particle of a string carrying a travelling wave is given b

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The displacement of a particle of a string carrying a travelling wave is given by y= (3.0 cm) sin 6.28(0.50x - 50 t),
where x is in centimeter and t in second. Find
(i) the amplitude (p) 50
(ii) the wavelength (q) 3
(iii) the frequency(r) 2
(iv) the speed (s) 100

Options:

A . (i) - (r); (ii) - (p); (iii) - (s); (iv) - (q)

B . (i) - (q); (ii) - (r); (iii) - (p); (iv) - (s)

C . (i) - (p); (ii) - (q); (iii) - (r); (iv) - (s)

D . (i) - (s); (ii) - (r); (iii) - (q); (iv) - (p)

Answer: Option B
:
B
The standard wave equation for a wave is

y = A s i n (k x - ω t)

Given equation

y = 3 s i n 6.28 (0.5 x - 50 t)

\Rightarrow y = 3 s i n (6.28 \times 0.5 x - 6.28 \times 50 t)

Comparing we get
amplitude A = 3 cm
Right here, we can see that B is the only possible option, but we may as well calculate the other values too.
Wave number

k = \frac{2 π}{λ} = 6.28 \times 0.5

\Rightarrow λ = \frac{2 π}{k} = 2 c m

Angular frequency

ω = 6.28 \times 50

Frequency

f = \frac{1}{T} = \frac{ω}{2 π} = \frac{6.28 \times 50}{2 \times 3.14}

f = 50 H z

wave speed =

\frac{λ}{T} = 2 \times 50 = 100 \frac{c m}{s}

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