Question

A transverse wave is found to have a vertical distance of 4 cm from a trough to a crest, a frequency of 12 Hz, and a horizontal distance of 5 cm from a crest to the nearest trough. Determine the amplitude, period, wavelength and speed of such a wave.

Answer 1

Answer:

Amplitude: 2cm

Period: 1/12 s

Wavelength: 10 cm

Speed: 120 cm/s

Explanation:

The amplitud is the vertical distance from the resting position to the crest or to the trough, and the vertical distance from a crest to a trough is two times the amplitude. Therefore the amplitud (A) is:

A= 4cm/2= 2cm

The period (T) is:

$T=\frac{1}{f}=\frac{1}{12}$ s

The wavelength is defined as the horizontal distance from a crest to the nearest crest or from a trough to the nearest trough. The distance from a crest to the nearest tough was given. Therefore two times that distance is the distance from a crest to the nearest crest.

The wavelenght (λ) is:

λ=(2)(5)=10cm

The speed (v) in a wave is given by:

v = λf

v=(10)(12)=120 cm/s