The vibrations of a string of length 60 cm fixed at both ends are represented by the…

PHYSICS · Multi-part · CBSE · Physics · Waves · Waves

Problem

The vibrations of a string of length 60 cm fixed at both ends are represented by the equation

y = 4 \sin \left( \frac{\pi x}{15} \right) \cos (96 \pi t)

where

x

and

y

are in cm and

t

in seconds. (1) What is the maximum displacement of a point at

x = 5 \text{ cm}

? (2) Where are the nodes located along the string? (3) What is the velocity of the particle at

x = 7.5 \text{ cm}

t = 0.25 \text{ sec.}

? (4) Write down the equations of the component waves whose superposition gives the above wave