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In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is $0.170\,\text{s}$ . The frequency of the wave is

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is

0.170\,\text{s}

. The frequency of the wave is

Understand relationship: Step $1$ : Understand the relationship between the time period and frequency. $\newline$ The time given ( $0.170$ second) is half the period of the wave, since it's only from maximum to zero displacement. To find the full period ( $T$ ), we need to double this time. $\newline$ Calculation: $T = 2 \times 0.170 = 0.34$ seconds.
Calculate period: Step $2$ : Calculate the frequency using the period. $\newline$ Frequency $f$ is the reciprocal of the period $T$ . So, $f = \frac{1}{T}$ . $\newline$ Calculation: $f = \frac{1}{0.34} \approx 2.94 \, \text{Hz}$ .

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