# Mechanical waves (frequency, period, wavelength, the wave speed) – problems and solutions

1. Two corks are on the crests of the waves. Both move up and down over the surface of sea 20 times in 4 seconds. If the distance of both corks is 100 cm and between them, there are two troughs and one crest, determine the wave frequency and the wave speed.

__Known :__

Both corks are at the tops of the waves and between the two corks, there are 2 troughs and 1 crest (see figure). So there are two wavelengths between the two corks.

Wavelength (λ) = 100 cm / 2 = 50 cm.

Frequency (f) = 20/4 = 5 Hertz

__Wanted:__ Frequency of wave and the wave speed

__Solution :__

The frequency of the wave (f) = 5 Hertz

The wave speed (v) = f λ = (5)(50 cm) = 250 cm/s

2. A spring (slinky) is vibrated to produce longitudinal waves where the distance between two closest compression = 40 cm. If the wave speed is 20 ms^{-1}, determine the wavelength and the wave frequency.

__Known :__

The distance between two closest compression = distance between two closest expansion = distance between two closest troughs = 1 wavelength

Wavelength (λ) = 40 cm = 0.4 m

The wavelength (v) = 20 m/s

__Wanted:__ Wavelength (λ) and frequency of the wave (f)

__Solution :__

Wavelength (λ) = 0.4 m

Frequency (f) = v / λ = 20 / 0.4 = 50 Hertz

3. At the surface of the sea, there are two corks separated from each other as far as 60 cm. Both corks move up and down 20 times in 10 seconds. When one is at the crest, other is at the trough of the wave. Between the two corks, there is a crest of a wave. Determine the wave period and the wave speed.

__Known :__

Wavelenght (λ) = 60 cm / 1.5 = 40 cm

Frequency (f) = 20/10 = 2 Hertz

__Wanted :__ Period and the wave speed.

__Solution :__

Period (T) = 1/f = 1/2 = 0.5 sekon

The wave speed (v) = f λ = (2)(40) = 80 cm/s