(a) A wave has a frequency of 800 MHz and a wave length of 30 cm. Calculate velocity.

(b) A radio can tune in to any station in 17.5 MHz to 13.5 MHz band, what is the corresponding wavelength band?

(a) As we know,

Velocity of wave (c) = frequency (f) x wavelength (λ)

Given,

f = 800 MHz

Hence, f = 800 x 10⁶ Hz or

f = 8 x 10⁸ Hz

λ = 30 cm

As 100 cm = 1m

Therefore,

30 cm = $\dfrac{30}{100}$ m

Hence, λ = 0.3 m

Substituting the values in the formula above we get,

c = 8 x 10⁸ x 0.3 = 2.4 x 10⁸ ms^-1

Hence,

Velocity of wave = 2.4 x 10⁸ ms^-1

(b) As we know,

Velocity of wave (c) = frequency (f) x wavelength (λ)

Given,

f = 17.5 MHz = 17.5 x 10⁶ Hz

Speed of light in air/vacuum = 3 x 10⁸ ms^-1.

λ = ?

Substituting the values in the formula above we get,

$3 \times 10^8 = (17.5 \times 10^6) \times λ \\[0.5em] \Rightarrow λ = \dfrac{ 3\times 10^8}{17.5 \times 10^6 } \\[0.5em] \Rightarrow λ = 17.1 \text{ m}$

Hence, wavelength of wave = 17.1 m

When,

f = 13.5 MHz = 13.5 x 10⁶ Hz

Speed of light in air/vacuum = 3 x 10⁸ ms^-1.

λ = ?

Substituting the values in the formula above we get,

$3 \times 10^8 = (13.5 \times 10^6) \times λ \\[0.5em] \Rightarrow λ = \dfrac{ 3\times 10^8}{13.5 \times 10^6 } \\[0.5em] \Rightarrow λ = 22.2 \text{ m}$

wavelength of wave = 22.2 m

∴ The corresponding wavelength band is 17.1 m - 22.2 m.