Question

The equation for the displacement of a stretched string is given by : y = 4 sin 2p$\left( \frac{t}{0.02}–\frac{x}{100} \right)$

Where y and x are in cm and t in sec. The

(i) Frequency (ii) Velocity of the wave

(iii) Maximum particle velocity are –

• A. 50 Hz, 50 m/s, 20p m/s
• B. 50 Hz, 20 m/s, 50 m/s
• C. 50 Hz, 50 m/s, 2p m/s
• D. 50 Hz, 50 m/s, 4p m/s

Answer 1

Answer: (D)

50 Hz, 50 m/s, 4p m/s

Answer 2

y = 4 sin $2\pi\left( \frac{t}{0.02}–\frac{x}{100} \right)$

compare it with the standard eqⁿ

y = A sin 2p $\left( \frac{t}{T}–\frac{x}{\lambda} \right)$

So T = 0.02 sec

n = $\frac{1}{T}$ = $\frac{1}{0.02}$ = 50 Hz .....(i)

l = 100 cm = 1 m

Wave velocity v = nl = 50 m/sec

Maximum particle velocity V_max = Aw

= 4 (2p × 50) = 400 p cm/sec

= 4p m/sec