Question

Show your solution in each question below:

1) The speed of an ocean wave on the coast is 42 m/s; the wavelength is 1.5 m. What is the frequency with which the wave hits the beach?

2) Radio waves travel at the speed of light, 3 x 10⁸ m/s. What is the wavelength of a radio wave from an AM station broadcasting at a frequency of 750 Hz? Find the wavelength in meter and kilometer.

3) A standing wave in a clothesline has 3 loops. . The clothesline is 12 m long and is vibrating at 0.5 vibrations per second. What is the speed of the wave?

Answer 1

1) We can find the frequency with which the wave hits the beach from the wave speed formula:

$$v=f\lambda,$$ $$f=\dfrac{v}{\lambda}=\dfrac{42\ \dfrac{m}{s}}{1.5\ m}=28\ Hz.$$

2)

$$\lambda=\dfrac{c}{f},$$ $$\lambda=\dfrac{3\cdot10^8\ \dfrac{m}{s}}{750\cdot10^3\ Hz}=400\ m=0.4\ km.$$

3) Let's first find the wavelength of the wave:

$$L=\dfrac{1}{2}n\lambda=\dfrac{3}{2}\lambda=1.5\lambda,$$ $$\lambda=\dfrac{L}{1.5}=\dfrac{12\ m}{1.5}=8\ m.$$

Finally, we can find the speed of the wave from the wave speed formula:

$$v=f\lambda=0.5\ Hz\cdot8\ m=4\ \dfrac{m}{s}.$$