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  • 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 is in s. The positive direction of x is from left to right.

A transverse harmonic wave on a string is described by y (x,t ) = 3.0 \sin \left (36t + 0.018x + \frac{\pi}{4} \right ) where x and y are in cm and t is in s. The positive direction of x is from left to right.
(a) The wave is travelling from right to left.
(b) The speed of the wave is 20 m/s.
(c) Frequency of the wave is 5.7 Hz.
(d) The least distance between two successive crests in the wave is 2.5 cm.

Answers (1)

The answer is the option (a), (b), and (c)

The standard form of a wave propagating in a positive direction

y=a \sin(\omega t-kx+\phi)and

 y = 3.0 \sin \left (36t + 0.018x + \frac{\pi}{4} \right )

A positive sign in the equation shows that the wave is travelling from right to left.

\omega =36 ;2\pi \nu=36 or v=\frac{36}{2\pi } =\frac{18}{3.14}=5.7Hz

k=0.018=\frac{2\pi }{\lambda }

\lambda =\frac{2\pi}{0.018}

 v=\nu \lambda =\frac{18}{\pi} \times \frac{2\pi}{0.018} =\frac{2000cm}{s}=\frac{20m}{s}

Distance between two successive crests=\lambda =\frac{2\pi }{0.018}=\frac{\pi}{0.009} =3.14\times \frac{1000}{9}=\frac{3140}{9}cm=348.8cm

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