A speaker plays a 100 Hz tone into a room where sound travels at 340 m/s. How long is each sound wave?
The 340 m/s and the 100 Hz both live inside v = fλ; this time the unknown is λ. After this last arrangement, all three unknowns can be found, and the practice mixes them.
Write down what is known: v = 340 m/s, f = 100 Hz, λ = ?
Write down the equation: v = fλ.
Substitute and calculate: λ = 340 ÷ 100 = 3.4. Each sound wave is 3.4 m long.
Now the whole family is in hand. v alone: v = fλ. f alone: f = v ÷ λ. λ alone: λ = v ÷ f.
Read each question for its unknown first. Pick the arrangement where that unknown stands alone, then substitute and calculate, and give the answer with its unit.
A speaker plays a 100 Hz tone, and the sound travels at 340 m/s. Calculate the wavelength.
Write down the values:
v = 340 m/s, f = 100 Hz, λ = ?
Write down the equation:
v = fλ
Make λ the subject:
λ = v ÷ f
Substitute in the values, and calculate:
λ = 340 ÷ 100 = 3.4
Each wave is 3.4 m long.
On a long spring, waves have frequency 20 Hz and wavelength 0.4 m. Calculate the wave speed.
Write down the values:
f = 20 Hz, λ = 0.4 m, v = ?
Write down the equation:
v = fλ
Substitute in the values, and calculate:
v = 20 × 0.4 = 8
The wave speed is 8 m/s.
A ship's horn sends sound through air at 340 m/s with frequency 85 Hz. Enter the wavelength, in m.
Waves on a bungee cord have frequency 6 Hz and wavelength 0.7 m. Enter the wave speed, in m/s.
Waves cross a bay at 7 m/s, with neighboring crests 3.5 m apart. Enter the frequency, in Hz.
An underwater buzzer sends sound through a pool at 1500 m/s with frequency 600 Hz. Enter the wavelength, in m.
Waves travel along a slack chain at 2.1 m/s with frequency 3.5 Hz. Enter the wavelength, in m.
A flagpole's rope carries waves at 5.4 m/s with wavelength 0.45 m. Enter the frequency, in Hz.
Hale's subwoofer plays a 40 Hz tone in a room where sound travels at 340 m/s. Enter the wavelength of the sound wave, in m.
A rescue rope stretched between two docks carries waves traveling at 4.8 m/s with wavelength 1.6 m. Enter the frequency, in Hz.
Ripples with frequency 7.5 Hz and neighboring crests 0.44 m apart cross a pond. Enter the wave speed, in m/s.