Wave speed

Wave speed is the speed at which energy is transferred, or the wave moves, through a medium. You must recall this equation:

wave speed = frequency × wavelength, or v = fλ

Example 1: a water wave has a frequency of 2 Hz and a wavelength of 0.5 m.

1. v = fλ = 2 × 0.5
2. v = 1 m/s

Example 2: sound travels at 330 m/s. Find the wavelength of a 1.1 kHz note.

1. Convert: 1.1 kHz = 1100 Hz
2. Rearrange: λ = v ÷ f = 330 ÷ 1100
3. λ = 0.3 m

Method:

1. Stand at least 100 m from a partner, and measure the distance with a trundle wheel.
2. Your partner bangs two cymbals together, high above their head.
3. Start a stopwatch when you see the cymbals meet, and stop it when you hear the sound.
4. Speed = distance ÷ time.

Light arrives almost instantly, so the time is how long the sound took. Repeat several times and find the mean, because your reaction time causes errors. A bigger distance makes these errors smaller compared with the time you measure.

1. Fill a ripple tank with water about 1 cm deep. Put a lamp above it, so the waves cast shadows on paper on the floor or bench below.
2. Turn on the motor that dips a bar into the water to make waves. A signal generator sets the frequency.
3. To measure wavelength: put a ruler on the paper, measure across 10 wave shadows, and divide by 10.
4. To measure frequency: count the waves passing a point in 10 s, and divide by 10 (or read it from the signal generator).
5. Calculate v = fλ.

Taking a photo of the shadows with a ruler in the picture "freezes" the waves, which makes them easier to measure.

1. Attach a string to a vibration generator, run it over a pulley and hang masses on the end to keep it tight.
2. Connect the vibration generator to a signal generator.
3. Adjust the frequency until you see a clear, still wave pattern of loops.
4. Measure across as many whole loops as you can. Each loop is half a wavelength, so work out λ.
5. Read the frequency from the signal generator, and calculate v = fλ.

• Independent variable: the frequency.
• Dependent variable: the wavelength.
• Control variables: the mass hung on the string (its tension) and the length of string.

Hazard: the masses could fall, so put padding underneath. In the ripple tank, keep water away from the electrics.

Improving accuracy: measure across many wavelengths and divide, rather than measuring one.