The Wave Equation

1. Water waves travel at 47 cm/s on the surface of a pond. If the wavelength is 7 cm, calculate the frequency of the waves.



2. A sound wave travelling through water is found to have a wavelength of 5.64 m. Its frequency is 262 Hz.
   1. Calculate the speed of this wave.
   2. How many times faster is this than the speed of sound in air?
   3. Can you suggest an explanation for your answer to part (ii)?
   ?



3. Draw a diagram of a wave which shows:
   1. Four complete wavelengths.
   2. Label any distance which shows the amplitude of the wave.
   3. Label one peak and one trough
   4. Label one complete wavelength



4. Draw pairs of diagrams to show the difference between waves with:
   1. High frequency and low frequency.
   2. High amplitude and low amplitude



5. The speed of radio waves is 3 x 10⁸ m/s (same as light). Find the wavelength for:
   1. an AM radio station, f = 1000 kHz
   2. an FM radio station, f = 100 MHz



6. 1. Calculate the frequency of a sound wave with l = 1.22 m (this is D above middle C on the piano if the speed of sound in air is 347 m/s)
   2. The range of human hearing is from about 20 Hz to 20 000 Hz. What is the corresponding range of wavelengths for
      1. sound in air, v = 330 m/s
      2. sound in water, v = 1480 m/s



7. 1. A wave with frequency 17 Hz and wavelength 2.47 m is emitted by a source. How far will one peak of this wave travel in 3 seconds?
   2. Is this a sound, light or water wave?