Question

Suppose a plot of 1/λ vs f has a slope of 0.728, what is the wave velocity? Give only the numerical answer with 4 decimal place without units. Answer will be graded to within +/- 0.1 of the correct answer so do not round until the final answer.

Answer 1

Answer:

1.3736

Explanation:

The velocity (v) of a wave is given by the product of the frequency (f) and the wavelength (λ) of the wave; i.e

v = fλ           ------------------(i)

Now, the slope of 1/λ vs f implies that;

1/λ is on the vertical axis;

f is on the horizontal axis;

such that the slope s will be given as;

s = 1/λ ÷ f

s = (1/λ) x (1/f)

s = 1/(fλ)     -----------------------(ii)

Since v = fλ from equation (i), substitute this into equation (ii) as follows;

s = 1 / v        -------------------------(iii)

From the question, s = slope = 0.728

Substitute this value of s into equation (iii) as follows;

0.728 = 1 / v

Solve for v;

v = 1 / 0.728

v = 1.3736

Therefore, the wave velocity is 1.3736

Answer 2

Answer:

The wave velocity is 1.3736

Explanation:

A plot of inverse of wavelength (λ) versus frequency (f), can be analyzed as follows;

The vertical axis will be 1/λ and the horizontal axis will be f

slope = (Δ1/λ)/(Δf)

        = 1/(fλ)

∴ 1/(fλ) = 0.728

From wave equation, V = fλ

where;

V is the wave velocity

f is the frequency of the wave

λ is the wavelength

1/(fλ) = 0.728

1/(V) = 0.728

V = (0.728)⁻¹

V = 1.3736

Therefore, the wave velocity is 1.3736