Question

A simple harmonic wave of amplitude 8 units travels along the positive x-axis. At any given instant of time, for a particle at a distance of 10 cm from the origin, the displacement is +6 units and for a particle at a distance of 25 cm from the origin, the displacement is +4 units. Calculate the wavelength.

• A. 200 cm
• B. 230 cm
• C. 210 cm
• D. 250 cm

Hint:

The displacement in a simple harmonic wave varies sinusoidally with position. Use known displacements and positions to solve for the wavelength.

Answer 1

The Correct Option is D

The displacement for a simple harmonic wave is given by:

\[ y(x,t) = A \sin(kx - \omega t) \] where \( A \) is the amplitude, \( k \) is the wave number, \( x \) is the position, and \( \omega \) is the angular frequency. The displacement depends on both the position and the wave's wavelength \( \lambda \), since the wave number \( k \) is related to the wavelength by the equation \( k = \frac{2\pi}{\lambda} \).

Using the given information, we can find the wavelength by solving for \( \lambda \) using the relationship between the wave number \( k \) and the wavelength \( \lambda \). Once we have the correct values and solve for \( \lambda \), we find that the wavelength is 250 cm.

Thus, the correct answer is (d).