Question

A transverse harmonic wave on a string is described by y(x, t) = 3 sin$\left( 36t + 0.018x + \frac{\pi}{4} \right)$ where x and y are in cm and t is in s. Which of the following statements is incorrect?

• A. The wave is travelling in negative x-direction
• B. The amplitude of the wave is 3 cm.
• C. The speed of the wave is 20 m s–1
• D. The frequency of the wave is $\frac{9}{\pi}$ Hz.

Answer 1

Answer: (D)

The frequency of the wave is $\frac{9}{\pi}$ Hz.

Answer 2

The given transverse harmonic wave equations is

$y = 3\sin\left( 36t + 0.018x + \frac{\pi}{4} \right)$ ….. (i)

As there is positive sign between t and x terms therefore the given wave is travelling in the negative x directions. The standard transverse harmonic wave equations is

$y = a\sin(\omega t + kx + \varphi)$ ….. (ii)

Comparing (i) and (ii) we get

$a = 3cm,\omega = 36rads^{- 1},k = 0.018radcm^{- 1}$

$\therefore$Amplitude of wave, a = 3 cm

Frequency of the wave,

$\upsilon = \frac{\omega}{2\pi} = \frac{36}{2\pi} = \frac{18}{\pi}Hz$

Velocity of the wave

$v = \frac{\omega}{k} = \frac{36rads^{- 1}}{0.018radcm^{- 1}} = 2000cms^{- 1} = 20ms^{- 1}$