First slide

Standing waves

Question

The vibrations of a string of length 60 cm fixed at both ends are represented by $y = 4 \sin (\frac{π x}{15}) \cos (90 π t)$ , where x and y are in cm and t is in second. Then velocity of component waves in the string is

Easy

A

13.5 m/s
B

18.5 m/s
C

24.5 m/s
D

48.5 m/s

Solution

Comparing the given equation with the equation of standing wave $y = A \sin K x . \cos ω t$ , we can write $K = \frac{π}{15} m^{- 1}$ and $ω = 90 π r a d / s$ .
$∴ V = \frac{ω}{K} = \frac{90 π}{π / 15} c m / s = 13.50 m / s$

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