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Question 48

A transverse wave on a string is described by $$y = 3\sin(36t + 0.018x + \pi/4)$$, where $$x$$, $$y$$ are in cm and $$t$$ in seconds. The least distance between the two successive crests in the wave is _______ cm. (Nearest integer) ($$\pi = 3.14$$)

Correct Answer: 349

Solution

Given wave:

$$y=3\sin(36t+0.018x+\pi/4)$$

Compare with standard form:

$$y=A\sin(ωt\pm kx+φ)$$

So,

k = 0.018 rad/cm

Distance between two successive crests = wavelength:

$$\lambda=\frac{2\pi}{k}$$

$$\lambda=\frac{2\times3.14}{0.018}=\frac{6.28}{0.018}$$

$$\lambda\approx348.9\text{ cm}$$

$$\lambda\approx349$$

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