Question

Which has the shorter time period--a pendulum
oscillating at a frequency of 1 Hz or one oscillating
at a frequency of 2 Hz?​

Answer 1

Required Answer:

→ A pendulum oscillating at a frequency of 2 Hz.

_______________________________

Here, we have to find which pendulum has shorter time period.

Given:

• A pendulum is oscillating at a frequency of 1 Hz .

• Another pendulum makes is oscillating at a frequency of 2 Hz .

To find:

• Which has the shorter time period?

Calculation:

We have to find time period in both cases in order to find which one has the shorter time period.

${\underline {\boxed {\Large {\bf { Case \: 1} }}}}$

• Frequency of the pendulum = 1 Hz

We know that,

★ $\boxed{\sf { T = \dfrac{1}{Frequency}}}$

→ $\sf { \dashrightarrow T = \dfrac{1}{1}}$

→ $\boxed{\sf \red{ \dashrightarrow T =1 \: s}}$

${\underline {\boxed {\Large {\bf { Case \: 2} }}}}$

• Frequency of the pendulum = 2 Hz

We know that,

★ $\boxed{\sf { T = \dfrac{1}{Frequency}}}$

→ $\sf { \dashrightarrow T = \dfrac{1}{2}}$

→ $\boxed{\sf \red{ \dashrightarrow T =0.5\: s}}$

From these observations, we can conclude that,

• 1 s > 0.5 s

Time period in Case I > Time period in Case II

⇒ Therefore, a pendulum oscillating at a frequency of 2 Hz has shorter time period.

_______________________________

Explore More !!

• Frequency is one of the characteristics of vibration.

• It determines the pitch of the sound.

• It is equivalent to number of oscillations made by body in given time.

• SI unit of frequency is Hertz (Hz)

• ★ $\boxed{\sf { Frequency = \dfrac{no. \: of \: oscillations }{time}}}$

• Time period is the time taken by the body to complete one oscillation.

• Time period (T) is equal to the reciprocal of the frequency.

• SI unit of time period is second (s).

• ★ $\boxed{\sf { T = \dfrac{1}{Frequency}}}$

Answer 2

Required Answer :-

➝ A pendulum oscillating at a frequency of 2 Hz.

_______________________________

Here, we have to find which the pendulum has shorter time period.

Given :-

• A pendulum is a oscillating at a frequency of 1 Hz.
• Another pendulum makes it oscillating at a frequency of 2 Hz.

To find :-

• Which has the shorter time period ?

Calculating :

We have to find time period in both cases in order to find which one has the shorter time period.

$\boxed{\bf\underline{Case~1}}$

• Frequency of the pendulum = 1 Hz.

★ We know that,

★ $\boxed{\sf{T = \frac{1}{Frequency} }}$

➝ ${\sf{T = \frac{1}{1}}}$

➝ $\boxed{\sf\purple{T = 1~s}}$

$\boxed{\bf\underline{Case~2}}$

• Frequency of the pendulum = 2 Hz.

★ We know that,

★ $\boxed{\sf{T = \frac{1}{Frequency} }}$

➝ ${\sf{T \: = \: \frac{1}{2}}}$

➝ $\boxed{\sf\purple{T = 0.05 s}}$

From these observations, we can conclude that,

• 1 s > 0.5 s

Time period in case l > Time period in case ll

➜ Therefore a pendulum oscillating at a frequency of 2 Hz has shorter time period.

_______________________

Explore More !!

• Frequency is one of the characteristics of vibration.

• It determines the pitch of the sound.

• It is to equivalent to number of oscillations made by body in given time.

• SI unit of frequency is Hertz (Hz).

★ $\boxed{\sf{Frequency = \frac{no.~of~oscillations}{time} }}$

• Time period is the time taken by the body to complete one oscillation.

• Time period (T) is equal to the reciprocal of the frequency.

• SI unit of time period is second (s).

★ $\boxed{\sf{T = \frac{1}{Frequency} }}$