# Transverse and longitudinal waves – problems and solutions

1. A wave is traveling down a 3-m long wire for 0.3 seconds. What is the period of the wave?

__Known :__

Time interval (t) = 0.3 seconds

__Wanted :__ Period (T)

__Solution :__

1 wavelength = 1 crests + 1 troughs

Period = 2 x 0.1 second = 0.2 seconds

2. The wave speed according to figure below is…

__Known :__

1 wavelength has 1 crests and 1 troughs. According to figure above, 1 wavelength = 2 meters x 4 = 8 meters.

Periode of wave (T) = 0.5 x 4 = 2 seconds

__Wanted :__ The wave speed (v)

__Solution :__

The wave speed :

v = s / t = λ / T = 8 meters / 2 seconds = 4 meters/second

3. The distance between point A and B is 30 cm. What is the wave speed according to figure below.

__Known :
__

From A to B, there is ¾ wavelength. If the distance between A and B is 30 cm, then the distance of ¼ wavelength is 30 cm / 3 = 10 cm. Thus, 1 wavelength = 4 x 10 cm = 40 cm.

According to the figure above, a period of the wave is 4 seconds.

__Wanted :__ The wave speed (v)

__Solution :__

v = d / t = λ / t

*v = the wave speed, d = distance, λ = wavelength, t = time interval*

The wave speed :

v = λ / t = 40 cm / 4 seconds = 10 cm / 1 second = 10 cm/second

4. If the distance of A and B = 250 cm, then the wave speed is…

__Known :__

Distance of A and B = 5/4 wavelength = 250 cm.

1/4 wavelength = 250 cm / 5 = 50 cm

1 wavelength = 4/4 wavelength = 4 x 50 cm = 200 cm

Period (T) = 2 seconds

__Wanted :__ The wave speed

__Solution :__

Formula of the wave speed :

v = d / t = λ / t

*v = the wave speed, d = distance λ = wavelength, t = time interval*

The wave speed :

v = 200 cm / 2 seconds = 100 cm/second

5. Amplitude of wave are shown by….

Solution :

The amplitude of the wave is BB’ and DD”.