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  • The displacement of a string is given by y (x,t) = 0.06 sin (2πx/3) cos (120πt) where x and y are in m and t in s. The length of the string is 1.5m and its mass is 3.0 10-2 kg (a) It represents a progressive wave of frequency 60Hz.

The displacement of a string is given by
y (x,t) = 0.06 \sin \left (\frac{2 \pi x}{3} \right ) \cos (120\pi t)
where x and y are in m and t in s. The length of the string is 1.5m and its mass is 3.0 \times 10^{-2} kg
(a) It represents a progressive wave of frequency 60Hz.
(b) It represents a stationary wave of frequency 60Hz.
(c) It is the result of superposition of two waves of wavelength 3 m, frequency 60Hz each travelling with a speed of 180 m/s in opposite direction.
(d) Amplitude of this wave is constant.

Answers (1)

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

Equation of stationary wave is y(x,t)=a \sin\left (kx \right )\cos\left (\omega t \right )

Since the waves are stationary, the amplitude varies from 0 to a=0.06m from nodes to antinodes.

Comparing this equation with the given equation y (x,t) = 0.06 \sin \left (\frac{2 \pi x}{3} \right ) \cos (120\pi t) 

We get\omega =120\pi =2\pi \nu ; \nu=60Hz

From equation \frac{2\pi }{3}=k=\frac{2\pi }{\lambda}

\lambda =3m, \nu =60Hz

Speed = 60\times 3=180m/s

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