Waves - Wave Equation

A radio station broadcasts at a frequency of $90 \times 10^6 \text{ Hz}$. If the speed of radio waves is $3.0 \times 10^8 \text{ m/s}$, calculate the wavelength of the radio waves.

Given: $f = 90 \times 10^6 \text{ Hz}$ and $v = 3.0 \times 10^8 \text{ m/s}$ Using the rearranged wave equation: $\lambda = \frac{v}{f}$ $\lambda = \frac{3.0 \times 10^8}{90 \times 10^6}$ $\lambda = \frac{300 \times 10^6}{90 \times 10^6}$ $\lambda \approx 3.33 \text{ m}$

To find the wavelength, we divide the wave speed by the frequency. Ensure that both values are in standard scientific notation for easier calculation.

A student observes water waves hitting a pier. The waves have a wavelength of $2.5 \text{ m}$ and a period of $0.5 \text{ s}$. Calculate the speed of these waves.

Given: $\lambda = 2.5 \text{ m}$ and $T = 0.5 \text{ s}$ Method 1: Using wave speed and period $v = \frac{\lambda}{T}$ $v = \frac{2.5}{0.5}$ $v = 5 \text{ m/s}$ Method 2: Finding frequency first $f = \frac{1}{T} = \frac{1}{0.5} = 2 \text{ Hz}$ $v = f \lambda = 2 \times 2.5 = 5 \text{ m/s}$

The speed of a wave can be calculated directly by dividing wavelength by the period, or by first finding the frequency and then multiplying it by the wavelength.

A sound wave travels at $340 \text{ m/s}$ with a wavelength of $0.17 \text{ m}$. Calculate the frequency of the sound wave.

Given: $v = 340 \text{ m/s}$ and $\lambda = 0.17 \text{ m}$ Using the rearranged wave equation: $f = \frac{v}{\lambda}$ $f = \frac{340}{0.17}$ $f = 2000 \text{ Hz}$

To solve for frequency, divide the wave speed by the wavelength. The resulting unit is Hertz ($Hz$).