First slide

Travelling wave

Question

A progressive wave is given by $y = 3 \sin 2 π [(t / 0 .04) - (x / 0 .01)]$ where x, y are in cm and t in s. The frequency of wave and maximum acceleration will be:

Moderate

A

$100 Hz, 4 .7 \times 10^{3} m / s^{2}$
B

$50 Hz, 7 .5 \times 10^{3} c m / s^{2}$
C

$25 Hz, 4 .7 \times 10^{4} m / s^{2}$
D

$25 Hz, 7.4 \times 10^{4} c m / s^{2}$

Solution

We know $ω = 2 πf = \frac{2 π}{0 .04}$
$\Rightarrow f = 25 Hz$
Differentiating y w.r.t. twice, we have
$y^{''} \frac{- 3 \times 4 π^{2}}{(0 .004)^{2}} \sin (2 π [(\frac{t}{0 .04}) - (\frac{x}{0 .01})])$
Maximum acceleration
$a_{m a x} = \frac{3 \times 4 π^{2}}{(0 .004)^{2}} c m / s^{2} = 7.4 \times 10^{4} c m / s^{2}$

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