Question

If you steadily shake one end of the taught rope three times each second, what would be the period of sinusoidal waves set up in the rope?

Answer 1

Hint:In order to solve this question we need to understand frequency, time period of wave, and wave. So a frequency is defined as the number of oscillations a wave performs in one second and time period defined as the period after which the wave pattern repeats itself.

Complete step by step answer:
A wave is defined as disturbance produced in a medium, there are two types of wave one is longitudinal wave and the other is transverse wave. Longitudinal waves are those waves in which vibration and direction of propagation of waves are both in the same direction, like sound waves. Transverse waves are those waves in which vibration and wave propagation are perpendicular to each other, like electromagnetic waves.

Given the problem: you shake three times each second so the number of revolutions per second is $3$. Since we know frequency is defined as the number of oscillations per second, so $f = 3Hz$. Let the time period of sinusoidal waves in rope be, $T$. Since we know the relation between frequency and time period as,
$f = \dfrac{1}{T}$
Hence the time period is,
$T = \dfrac{1}{f}$
Putting values we get,
$T = \dfrac{1}{3}\sec \\$
$\therefore T = 0.3334\sec $

So the time period of the sinusoidal wave is $0.3334\sec $.

Note:It should be remembered that wavelength of sound wave or any other wave can also be determined from frequency of wave, as wavelength is mathematically defined as the ratio of wave speed to the frequency of wave, and it physically means that wavelength is distance between consecutive crest or trough of wave.