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JEE Main · 2023 · 10 Apr 2023 · Shift 1 · Waves & Sound

A transverse harmonic wave on a string is given by

y (x, t) = 5 sin (6 t + 0.003 x)

where

x

and

y

are in cm and

t

in sec. The wave velocity is

____

ms^{- 1}

.

Answer: 20

Solution

Writing the wave as

y = A sin (ω t + k x)

gives

ω = 6 rad s^{- 1}

and

k = 0.003 cm^{- 1}

. The wave speed is

v = \frac{ω}{k} = \frac{6}{0.003} = 2000 cm s^{- 1}

. Converting to SI, the wave velocity is

20 m s^{- 1}

.

JEE Main · 2023 · 10 Apr 2023 · Shift 1 · Integer answer

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