Question

Ram and Shayam stand $8m$ apart and demonstrate the motion of a transverse wave on a string. The wave can be described as having a vertical distance of $32cm$ from a trough to a crest, a frequency of $2.4Hz$, and a horizontal distance of $48cm$ from a crest to the nearest trough. Determine the amplitude, time period and wavelength of such a wave.

Answer 1

Step 1: Given data:

The vertical distance from a trough to a crest of the wave, $d_1=32cm$

Frequency, $f=2.4Hz$

The horizontal distance from a crest to the nearest trough, $d_2=48cm$

The diagram below demonstrates _.$d_1$and $d_2$.

Step 2: Determine the Amplitude of the wave:

The amplitude $\left(A\right)$ of a wave is defined as the maximum displacement of a particle from the equilibrium.

From the figure, $2A=d_1$

Therefore, $A=\frac{d_1}{2}$

Putting the value of $d_1$:

Amplitude, $A=322cm$

$=16cm$

Step 3: Determine the time period:

The frequency $\left(f\right)$ of a wave is the number of complete cycles a wave make in unit time.

The period and frequency of a wave are related by the following equation:

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

Putting $f=2.4Hz$ in the above equation:

$T=12.4s$

$=0.42s$

Step 4: Determine the wavelength-

The wavelength $\left(\lambda \right)$ of a wave is defined as the distance covered by the wave in a complete cycle.

From the figure, $\frac{\lambda }{2}=d_2$

Putting the value of $d_2$:

$\lambda =2\times 48cm$

$=96cm$
Hence, the amplitude, period, and wavelength of the wave are 16 cm, $0.42s$ and $96cm$ respectively.