Question

Consider two waves X and Y traveling in the same medium. The two carry the same amount of energy per unit time, but X has one-seventh the amplitude of Y. What is the ratio of their wavelengths? (λY/λX=?)

Answer 1

Answer:

7 / 1

Explanation:

The ratio of their amplitude = one-seventh and the ratio of their amplitude = the ratio of their wavelength

Ax / Ay = λx / λy  = 1 / 7

λy / λx = 7 / 1

Answer 2

The ratio of wavelengths is λ(y)/λ(x) = 1/49.

The energy of a wave is directly proportional to the square of the amplitude of the wave.

   E ∝ $A^{2}$ , where E is the energy of the wave and A is the apmlitude

We also know that enegy

E = hc/λ

E ∝ 1/λ

According to the question:

Let wave X has energy $E_x$ and amplitude $A_x$

and wave Y has energy $E_y$ and amplitude $A_y$

$\frac{E_x}{E_y}=\frac{A_x^2}{A_y^2} \\\\\frac{E_x}{E_y}= \frac{(A_y/7)^2}{A_y}\\\\\frac{E_x}{E_y}=\frac{1}{49}$ since it is given that $A_x=\frac{1}{7}A_y$

{1/λ(x)} / {1/λ(y)} = 1/49

λ(y)/λ(x) = 1/49 is the ratio of the wavelengths.

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