Simple Pendulum Experiment

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Questions and Answers

What does the term 'periodic motion' refer to in the context of a simple pendulum?

It is the repeating motion of an object returning to a given position after a fixed time interval. (correct)

It is a type of motion that only occurs in circular paths.

It represents the instantaneous motion of the pendulum at a certain point.

It is the motion of an object that does not return to its initial position.

Which equation correctly relates the frequency (f) and period (T) of a pendulum?

$T = \frac{1}{f^2}$

$f = 2 heta T$

$f = \frac{1}{T}$ (correct)

$T = 2 heta f$

How is the frequency of a simple pendulum mathematically expressed in terms of its length (L) and acceleration due to gravity (g)?

$f = \frac{2\pi}{gL}$

$f = \frac{2\pi}{L\sqrt{g}}$

$f = \frac{1}{2\pi} \sqrt{\frac{g}{L}}$ (correct)

$f = \frac{1}{2\pi} \sqrt{gL}$

What is the value of the acceleration due to gravity (g) used in the calculations for this experiment?

9.8 m/s² Signup and view all the answers

In a pendulum experiment, if the length of the string (L) doubles, how does it affect the period (T) of the pendulum?

The period increases by a factor of $rac{1}{\sqrt{2}}$. Signup and view all the answers

What is the relationship between the speed of sound in air and the temperature according to the given formula?

The speed of sound increases by 0.6 m/s for each degree Celsius increase in temperature. Signup and view all the answers

From the equations provided, what does 'n' represent in the context of resonance frequencies?

The harmonic number indicating modes of vibration. Signup and view all the answers

If the fundamental frequency is defined when n=1, what represents higher frequencies in this context?

Overtones for n=2. Signup and view all the answers

What is the formula for calculating the average speed of sound given a set of values?

Average speed = total of speed values divided by the number of values. Signup and view all the answers

Which method involves plotting 1/f on the x-axis and L on the y-axis?

Graphical method. Signup and view all the answers

How is the experimental value of the speed of sound, $v_{exp}$, calculated?

$v_{exp} = 4 × slope$. Signup and view all the answers

What is the speed of sound at 0°C, denoted as $v_0$?

331 m/s. Signup and view all the answers

What is the method for calculating the percentage error in velocity?

Compare the experimental velocity to theoretical velocity. Signup and view all the answers

For a tube of length 0.3 m closed at one end, which wavelength corresponds to the lowest tone produced?

0.6 m Signup and view all the answers

What is the fundamental frequency produced by a tube of length 1.0 m and sound speed of 80 m/s?

40 Hz Signup and view all the answers

In a converging lens, what is the sign of the focal length?

Always positive Signup and view all the answers

What happens to light rays in a diverging lens?

They diverge away from the axis. Signup and view all the answers

If the speed of sound at 0°C is 331 m/s, how do you calculate the speed of sound in air at 20°C?

Use the formula: speed = 331 + 0.6 * T Signup and view all the answers

What does the power of a converging lens depend on?

Curvature of the lens surfaces and its focal length Signup and view all the answers

How does a converging lens refract light rays?

Toward the lens axis Signup and view all the answers

What is the lowest overtone frequency for a tube of length 1 m closed at one end and with a speed of sound at 80 m/s?

160 Hz Signup and view all the answers

What does the power of a lens measure?

The bending of light rays through the lens Signup and view all the answers

If the focal length of a lens is increased, what happens to its power?

Power decreases Signup and view all the answers

Using the formula for power, what is the unit of power of a lens?

Diopter (D) Signup and view all the answers

What results from a high-power lens?

It bends light rays at a large angle Signup and view all the answers

What is the correct expression for calculating the focal length from object and image distances?

$f = \frac{s \cdot s'}{s + s'}$ Signup and view all the answers

What happens to the focal length when the power of the lens increases?

Focal length decreases Signup and view all the answers

If a lens has a focal length of 20 cm, what is its power?

5 D Signup and view all the answers

What is the main difference between a low-power lens and a high-power lens?

Low-power lenses bend light through a small angle Signup and view all the answers

How do you calculate the average focal length from multiple lenses?

Add all focal lengths and divide by the number of lenses Signup and view all the answers

Study Notes

Experiment 1: Simple Pendulum

Objective: To determine the acceleration due to gravity (g).
Theory:
- Periodic motion is the repeating motion of an object returning to a given position after a fixed time interval. Oscillations are these repetitive movements.
- A simple pendulum is a mechanical system exhibiting periodic motion. It consists of a particle-like bob of mass (m) suspended by a light string of length (L) fixed at the upper end.
- The period (T) of a pendulum is the time interval for one complete oscillation.
- The frequency (f) of a pendulum represents the number of oscillations per unit time interval.
- Frequency (f) and period (T) are related by the formula: f = N/t and T = t/N, where N is the number of complete oscillations and t is the total time in seconds.
- The frequency (f) and period (T) are also related by the following formula: f = 1/(2π)√(g/L) and T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.

Experiment 2: Speed of Sound

Objective: To determine the speed of sound in air.
Theory:
- Sound waves are longitudinal waves where the oscillations are along the direction of propagation.
- In a resonance tube (closed at one end), the distance between a node and an anti-node is λ/4. Resonance occurs when the length of the air column is equal to an odd number of λ/4.
- The wavelength (λ) and the length (L) of the air column are related by the formula: λ = 4L/n (where 'n' is an integer: 1, 3, 5, ...).
- The speed of sound (v) is related to frequency (f) and wavelength (λ) by the formula: v = fλ.
- The resonance frequency (fₙ) in a tube (air column) is related to its length (L) by the following equation: fₙ = nv/4L (where 'n' is an integer: 1, 3, 5...). The lowest frequency (n=1) is the fundamental frequency.
- The speed of sound in air is also influenced by temperature: v = v₀ + 0.6T where v₀ is the speed of sound at 0°C and T is the temperature in °C.

Experiment 3: Lenses

Objectives:
- To determine the focal length (f) of a converging lens.
- To determine the power (P) of a converging lens.
Theory:
- A lens is a transparent object that uses refraction to bend light rays.
- A converging lens refracts light rays toward its axis. A diverging lens refracts light rays outward from its axis.
- The focal length (f) of a lens is the distance from the center of the lens to its focal point. Focal length is positive for a converging lens and negative for a diverging lens.
- The power of a lens (P) is equal to the reciprocal of its focal length (P = 1/f). The SI unit of power is Diopters (D), and if focal length is in cm, then P = 100/f.

Experiment 4: Viscosity of Liquids

Objective: To measure the dynamic viscosity of a liquid using a falling sphere method (Stokes' method).
Theory:
- Viscosity is a fluid property resisting flow.
- Dynamic viscosity (μ) is the ratio of shear stress to shear rate.
- Shear stress (τ) is related to the force (F) acting on an area (A) τ = F/A).
- Shear rate (du/dy) is the rate of change in velocity with respect to distance.
- Stokes' Law describes the viscous drag (F_d) on a sphere moving through a fluid: F_d = 6πμrv, where μ is dynamic viscosity, r is the radius of the sphere, and v is the sphere's velocity.
- A falling sphere experiences gravitational force (W), buoyant force (F_b), and viscous drag (F_d). At terminal velocity, the net force is zero (W = F_b + F_d).
- The dynamic viscosity (μ) can be calculated from the terminal velocity (v_f) and other properties using the appropriate formulas.

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Description

This quiz focuses on the fundamentals of a simple pendulum and its role in determining the acceleration due to gravity. It covers key concepts such as periodic motion, oscillations, and the relationship between frequency and period. Test your understanding of these principles and the applicable formulas.