Density and Sound (UNITS 3.1 & 6.1) S2A Stage 9

Three units apart, three years closer.

Density is the measure of how many particles of matter there is in a specific volume. It is the measure of mass per unit volume. It’s how closely packed particles are in an object. 

What is Density?

Volume is how much space an object takes up or occupies. This includes all substances: solids, liquids and gases.

Define volume.

Mass is how much stuff (particles) is inside something (a substance). It tells us how much matter an object has/how much matter is inside an object.

Define Mass.

Weight is a reflection of gravity’s pull on an object.

Define Weight.

That means more stuff/particles (mass) is taking up those object’s space (volume), and is closely packed, more so than the other object.

What does it mean if something is denser than another object?

True.

TRUE/FALSE: An elevator with 15 people in it would be more dense than the same elevator with only 3 people in it.

Density = mass/volume

Mass = density x volume

Volume = mass/density

*Different items and substances have different densities. Density can impact the conversion from mass to volume and vice versa.

List the equation to find density.

kg/m³

What is the standard unit for density?

Water - 1g/ml OR 1g/cm³

Sucrose  - 1.58g/cm³

Sodium Chloride - 2.16g/cm³

Densities of Objects (IMPORTANT)

It will sink. This is because the density of the object is larger than the density of water. (x > 1g/cm³)

If something has a greater density than water, will it float or sink if its placed in water?

It will float. This is because the density of the object is smaller than the density of water. (x < 1g/cm³)

If something has a smaller density than water, will it float or sink when placed in water?

1. Density. As long as the object/liquid/gas/substance you are putting into any fluid/substance has a lower density than the said fluid (in terms of numerical value), then it will always FLOAT. If not, it will SINK. If an object's density is equal to the density of the fluid/water however, it will be neutrally buoyant, meaning it will neither sink nor float to the surface. Instead, it will remain suspended at whatever depth it is placed, as the upward buoyant force exactly balances the downward force of gravity. 

2. Law of Buoyancy. If the buoyant force of an object is greater than the force of gravity acting on that object, it will FLOAT. The buoyant force of an object is produced when fluid is displaced when the object is placed into the fluid. The pushing apart of the fluid creates a force pushing upwards on the object, which is now a buoyant force. The ship will also float when the buoyant force is equal to the weight of the ship.

3. Shape, Size and Surface Area.

4. Materials. If the object is made of steel, it will definitely have a density higher than an object made of Styrofoam when their masses are equal. This still links back to density.

How do we know if something can float or sink in a substance?

No. Mass stays the same wherever you are. This is because it is the measure of how much matter makes up an object. The matter does not change when its moved. Mass is measured in kilograms or grams.

Does mass change depending on location or gravity?

Yes. This is because weight is the measure of the how strong gravity pulls on the mass of an object. So, it will change depending on the force of gravity, and as gravity changes depending on location, it will vary depending on those two factors. Weight is measured in Newtons (N).

Does weight change depending on location and gravity?

Mass → How much STUFF

Weight → How heavy it FEELS

What’s a quick way to remember mass and weight?

On earth → Heavy

On moon → Light

In space → Floating

Difference of weight in different locations:

Density → Solids: g/cm³

Liquids: g/mL

Mass → Grams, Kilograms

Volume → Solids: cm³

Liquids: mL

Units for density, mass and volume?

Regular: Volume → s³ / length x width x height

Irregular: Water displacement method

The water displacement method involves submerging an object in water and measuring the amount of water it displaces. This method is based on Archimedes’ principle, which states that the amount of water displaced by an object is equal to the volume of an object.

How do I calculate volume for shapes?

The borderline is the density of the item for testing, the density fo the thing/fluid the object is put in.

What is the borderline?

If the honey has water mixed in, it will weigh lighter than the others as its density is lighter when mixed with water (the overall volume increases but the mass is lower as space needs to be made for water, so there’s less honey for more water). To check which jars have water mixed in them, simply weigh them one by one and choose the lightest jar.

Some jars of honey have water mixed in. Without opening any jars, how do you check which jars have water mixed in?

1. SOLIDS
   - Look at the structure. For example, in rocks, if it has a compact structure, it may have a higher density compared to porous (many-holed) rocks.

How do you know an object has a higher/lower density than other objects without weighing them?

Yes. For liquids, they will be more dense when temperature decreases. This is seen in cold ketchup being harder to pour out than hot ketchup. The ketchup becomes denser when it is colder because the lower temperature causes the particles to come closer.

This is possible because the particles in liquids are not fixed like in solids and are free to move.

For gases, hot air is LESS DENSE than cold air. This is because the particles move around more and they get faster, this increases the space the gas occupies, therefore increasing the volume and decreasing the density.

Gases become denser as temperature decreases because the gas molecules lose kinetic energy, slow down, and move closer together, which decreases the volume occupied by the gas for a fixed mass.

Does density differ in liquids and gases at different temperatures?

When a ship is placed on water, it pushes some water aside (displaced water). The displaced water pushes back on the ship with an upward buoyant force. The ship floats when this buoyant force equals the weight of the ship. (However, some ships will sink if the weight is too large.)

How can a heavy ship float on water?

Sound is a form of energy that we hear when something vibrates.

What is sound?

1. Mechanical Wave: It needs a medium (like air, water or solid) to travel through. Sound cannot travel through empty space (or vacuum).

2. Longitudinal Wave: The particles of the medium vibrate back and forth in the same direction that the wave is moving.

What are the properties of sound?

Energy is the ability to do work.

What is energy?

Mute people cannot talk as they can’t produce vibrations using their larynx (voicebox).

Why can’t mute people speak?

Sound is produced by means of vibrations. When the back and forth movement of particles reaches our ears, they cause our eardrums to vibrate.

As a result, part of our inner ear also vibrates. Our brain then detects this as a sound.

How are sounds produced, and how do we hear them?

A waveform is basically a visual or graphical representation of a wave.

What is a waveform?

An oscilloscope is an electronic test and measurement instrument that graphically displays electric signals in the form of an x plot.

What is an oscilloscope?

The amplitude is the height of a crest or depth of a trough. The distance of the crest to the equilibrium of the wave is the amplitude.

What is the amplitude of a wave?

A wave length is the length from one end of a crest to another, or the length of one trough/crest.

What is a wave length?

Compression is the area in a longitudinal wave where particles are closest together, resulting in high pressure.

Rarefaction is the area where particles are spread farthest apart, resulting in low pressure.

What is compression and rarefaction?

Decibels (dB). Sounds above 85 dB are harmful.

In what unit is loudness measured in?

Our range of hearing goes from 20 Hz to 20,000 Hz. Above 20 Hz is infrasonic. Over 20,000 Hz is ultrasonic.

What is the range of the frequency humans can hear?

Yes, a sound is louder if its amplitude increases. The amplitude of a sound wave is directly related to its loudness; a higher amplitude means more energy is transferred, which our ears perceive as a louder sound. Conversely, a smaller amplitude corresponds to a softer sound. 

Is a sound louder when amplitude is higher?

The frequency of sound is the number of times a sound pressure wave repeats itself or cycles per second, measured in Hertz (Hz). It determines the pitch of a sound, with higher frequencies resulting in a shriller tone and lower frequencies producing a deeper tone.

What is the frequency of sound?

The amplitude represents the LOUDNESS of a sound. The larger the amplitude, the louder the sound. The frequency represents the PITCH of a sound. The faster the frequency, the higher the pitch.

What do the amplitude and frequency represent in an oscilloscope trace?

The smaller the volume of water, the lower the pitch. The higher the volume of water, the higher the pitch.

This is due to the volume of air present in each water level, if the water level is high, the volume of air is small and the vibrations of the particles will be fast, producing a high pitch. If the water level is low, the volume of air is big and the vibrations of the particles will slow down as they bounce from one surface to the other.

When you blow over the top of a bottle with water in it, or if you hit it, what is the correlation between the volume of water in it and the pitch of the sound produced?

A trace (or wave trace) is a graphical representation of a wave, commonly seen in oscilloscopes.

What is a trace?

F = 1/T

T = 1/F

1 = FT

How do you calculate for frequency and the period of a wave?

A period is how long one cycle takes in a wave. It tells you how much time is required for one full cycle or vibration to occur. It is typically measured in seconds and is represented by the letter ‘T’.

For example, the period of a wave is the time between two successive crests or troughs.

What is a period in a wave?

Interference is an effect that occurs when two or more waves overlap.

In general, the individual waves do not affect one another, and the total wave amplitude at any point in space is simply the sum of the amplitudes of the individual waves at that point.

What is interference?

1. Constructive interference
   - It is a type of interference where the two interfering waves have a displacement in the same direction.
   - It is observed at any location where the two interfering waves are displaced upward.
   - It is also observed when both interfering waves are displaced downward.

2. Destructive interference
   - It is a type of interference where the two interfering waves have a displacement in the opposite direction.
   - If a crest of one wave meets a trough of another wave, then the magnitude of the displacements is equal to the difference in the individual magnitudes; this is known as destructive interference.

Types of Interference?

A wave is a disturbance or vibration that transfers energy from one place to another without moving matter from place to place.

What is a wave?

Constructive: To find the amplitude of a constructive interference wave, add the amplitudes of the individual waves together. This applies when the crests of two waves align with each other and the troughs align with each other, resulting in a new wave with a larger amplitude. 

Destructive: To find the amplitude of a destructive interference wave, subtract the amplitude of the second wave from the first.

𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒=|𝐴1−𝐴2|

How to find the amplitude of a constructive and destructive interference wave?

A wave cycle is one complete repetition of a wave's pattern, such as the motion from one peak to the next peak, or from one trough to the next trough.

What is a wave cycle?