The displacement of an elastic wave is given by the function

y = 3 sin ωt + 4 cos ωt.

where y is in cm and t is in second. Calculate the resultant amplitude.

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Payal Gupta | Contributor-Level 10

7 months ago

This is a short answer type question as classified in NCERT Exemplar

Displacement of an elastic wave y =3sinwt+4coswt

3= acos $\emptyset$

4=asin $\emptyset$

On dividing above equation

tan $\emptyset$ =4/3

$\emptyset = {t a n}^{-} (\frac{4}{3})$

a²cos^{2 $\emptyset$}+a²sin^{2 $\emptyset$}= 3²+4²

a² (cos^{2 $\emptyset + {s i n}^{2} \emptyset$})=25

a².1=25

a=5

Y= 5cos $\emptyset s i n w t$ +5sin $\emptyset c o s w t$

= 5 [cos $\emptyset s i n w t + s i n \emptyset c o s w t$ ]=5sin (wt+ $\emptyset$ )

$\emptyset = {t a n}^{- 1} (\frac{4}{3})$

Hence amplitude =5cm

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The displacement of an elastic wave is given by the function y = 3 sin ωt + 4 cos ωt. where y is in cm and t is in second. Calculate the resultant amplitude.

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