A wave is given by Y = 3sin 2π(t/0.04 - x/0.01) where Y is in cm. Frequency of the wave and maximum acceleration will be (π² = 10) (a) 100 Hz, 4.7 × 10⁴ cm/s² (b) 50 Hz, 7.5 × 10³ cm/s² (c) 25 Hz, 4.7 × 10⁴ cm/s² (d) 25 Hz, 7.5 × 10⁴ cm/s²

Answer: (d). Compare with Y = Asin 2π(t/T - (x)/(λ)): T = 0.04 s, f = 25 Hz, A = 3 cm. ω = 2π f = 50π rad/s amax = ω² A = 2500π² × 3 = 2500 × 10 × 3 = 7.5 × 10⁴ cm/s² So the answer is (d) 25 Hz, 7.5 × 10⁴ cm/s².

A wave is given by Y = 3sin 2π(t/0.04 - x/0.01) where Y is in cm… | MHT CET 2024 (15 May, Shift 2)

Q35MHT CET 2024 · 15 MAY · SHIFT 2Easy

Progressive Wave Equation

A wave is given by $Y = 3\sin 2\pi\left(\frac{t}{0.04} - \frac{x}{0.01}\right)$ where Y is in cm. Frequency of the wave and maximum acceleration will be $(\pi^2 = 10)$

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Answer: (d)

Compare with $Y = A\sin 2\pi\left(\dfrac{t}{T} - \dfrac{x}{\lambda}\right)$ : $T = 0.04\text{ s}$ , $f = 25\text{ Hz}$ , $A = 3\text{ cm}$ .
$\omega = 2\pi f = 50\pi\text{ rad/s}$
$a_{max} = \omega^2 A = 2500\pi^2 \times 3 = 2500 \times 10 \times 3 = 7.5 \times 10^{4}\text{ cm/s}^2$
So the answer is (d) $25\text{ Hz}$ , $7.5 \times 10^{4}\text{ cm/s}^2$ .

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Progressive Wave Equation question from MHT CET 2024 (15 May, Shift 2)

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