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🌊 Detailed Explanation of Wavelength, Frequency, Period, and Wave Speed
When studying waves in Year 10 Physics, it is important to understand the key terms: wavelength, frequency, period, and wave speed. These concepts are fundamental in the National Curriculum and are essential for analysing wave behaviour.
🌈 Wavelength (λ)
Wavelength is the distance between two consecutive points that are in phase on a wave, such as two crests or two troughs. It tells us how long one complete wave cycle is. The unit for wavelength is metres (m).
- Example: If you look at ocean waves, the wavelength is the distance from the top of one wave to the top of the next wave.
⏱️ Frequency (f)
Frequency is the number of complete waves (or cycles) that pass a fixed point in one second. Frequency is measured in hertz (Hz), where 1 Hz means one wave per second.
- Example: If 5 waves pass a point every second, the frequency is 5 Hz.
🕰️ Period (T)
The period is the time taken for one complete wave to pass a point. It is the reciprocal of frequency.
The unit for the period is seconds (s).
- Example: If the frequency of a wave is 10 Hz, the period is seconds.
🏃♂️ Wave Speed (v)
Wave speed is how fast the wave travels through the medium. It depends on the type of wave and the medium it moves through. The unit for wave speed is metres per second (m/s).
🔗 Relationship Between Wavelength, Frequency, Period, and Wave Speed
These terms are connected by the wave equation:
Where:
- v is the wave speed (m/s),
- f is the frequency (Hz),
- λ is the wavelength (m).
Since the period is the reciprocal of frequency, you can also express wave speed as:
🧮 Example Problem
If a wave has a frequency of 5 Hz and a wavelength of 2 metres, what is the wave speed?
Using the formula:
So, the wave travels at 10 metres per second.
💡 Study Tips for Understanding Waves
- Draw diagrams to visualise waves, marking wavelength and periods.
- Practice converting between frequency and period.
- Use real-life examples like water waves or sound waves to relate to concepts.
- Memorise the wave equation and units for each quantity.
By mastering wavelength, frequency, period, and wave speed, you will better understand how waves behave in different scenarios, which is a key part of the Year 10 Physics curriculum.
✍️ 10 Examination-style 1-Mark Questions on Wavelength, Frequency, Period, and Wave Speed
- What is the name of the distance between two consecutive crests in a wave?
Answer: Wavelength - What do we call the number of waves passing a point each second?
Answer: Frequency - What is the term for the time taken for one complete wave to pass a point?
Answer: Period - Which property of a wave is measured in metres per second (m/s)?
Answer: Speed - What is the symbol commonly used for frequency in physics?
Answer: f - If the frequency increases, what happens to the period?
Answer: Decreases - What type of wave property is wavelength: transversal or longitudinal?
Answer: Neither - Which quantity is calculated by dividing wavelength by period?
Answer: Speed - What unit is used to measure frequency?
Answer: Hertz - Which wave property is the reciprocal of frequency?
Answer: Period
📝 10 Examination-Style 2-Mark Questions on Wavelength, Frequency, Period, and Wave Speed
- Define wavelength in terms of a wave.
– Wavelength is the distance between two consecutive points in phase on a wave, such as crest to crest or trough to trough. - What is the unit of frequency in the International System (SI)?
– The unit of frequency is the hertz (Hz), which means one cycle per second. - Calculate the period of a wave with a frequency of 5 Hz.
– The period \(T = \frac{1}{f}\), so \(T = \frac{1}{5} = 0.2\) seconds. - How are frequency and period related?
– Frequency and period are inversely proportional, where frequency equals one divided by period. - What is wave speed if the wavelength is 2 m and the frequency is 3 Hz?
– Wave speed \(v = f \times \lambda = 3 \times 2 = 6\) m/s. - A wave has a period of 0.1 s; calculate its frequency.
– Frequency \(f = \frac{1}{T} = \frac{1}{0.1} = 10\) Hz. - State the formula that links wave speed, frequency, and wavelength.
– Wave speed \(v = f \times \lambda\). - A wave travels 12 metres in 3 seconds. Calculate its speed.
– Speed \(v = \frac{distance}{time} = \frac{12}{3} = 4\) m/s. - If a wave’s speed is 8 m/s and its wavelength is 4 m, what is its frequency?
– Frequency \(f = \frac{v}{\lambda} = \frac{8}{4} = 2\) Hz. - Explain why increasing the frequency of a wave decreases its period.
– Because period and frequency are inversely related, increasing frequency means the time for one cycle (period) becomes shorter.
🔍 10 Examination-Style 4-Mark Questions on Wavelength, Frequency, Period, and Wave Speed
Question 1
A wave has a frequency of 5 Hz and a wavelength of 2 m. Calculate the speed of the wave. Show your working.
Answer:
The wave speed (v) is calculated using the formula \( v = f \times \lambda \).
Given the frequency \( f = 5 \, \text{Hz} \) and wavelength \( \lambda = 2 \, \text{m} \),
Substitute the values: \( v = 5 \times 2 = 10 \, \text{m/s} \).
Therefore, the wave speed is 10 metres per second.
This means the wave travels 10 metres every second.
Question 2
Explain the relationship between frequency and period of a wave.
Answer:
Frequency is the number of waves that pass a point each second and is measured in hertz (Hz).
Period is the time taken for one complete wave to pass a point and is measured in seconds (s).
The frequency and period are inversely related, meaning when frequency increases, period decreases.
Mathematically, \( f = \frac{1}{T} \) or \( T = \frac{1}{f} \), where \( f \) is frequency and \( T \) is period.
If a wave has a high frequency, its period will be very short.
This is because the waves pass by more quickly.
Question 3
A wave has a period of 0.2 seconds. What is its frequency?
Answer:
Frequency is the inverse of the period.
So, \( f = \frac{1}{T} \), where \( T \) is the period.
Given \( T = 0.2 \, \text{s} \), substitute the value: \( f = \frac{1}{0.2} = 5 \, \text{Hz} \).
This means 5 waves pass a point every second.
Therefore, the frequency of the wave is 5 hertz.
Question 4
Describe what happens to the wave speed if the wavelength doubles but the frequency remains the same.
Answer:
Wave speed is given by \( v = f \times \lambda \).
If the frequency stays constant but the wavelength doubles,
The wave speed will also double because speed is directly proportional to wavelength.
For example, if the wavelength doubles from 2 m to 4 m, and frequency is 5 Hz,
Then the speed changes from \( 5 \times 2 = 10 \, \text{m/s} \) to \( 5 \times 4 = 20 \, \text{m/s} \).
This shows wave speed increases when wavelength increases if frequency does not change.
Question 5
Calculate the period of a wave with a frequency of 50 Hz.
Answer:
Period is the inverse of the frequency, given by \( T = \frac{1}{f} \).
Here, the frequency \( f = 50 \, \text{Hz} \).
Substituting, \( T = \frac{1}{50} = 0.02 \, \text{s} \).
So, the period of the wave is 0.02 seconds.
This means one complete wave passes every 0.02 seconds.
Question 6
A wave travels at a speed of 340 m/s and its frequency is 170 Hz. Find the wavelength of the wave.
Answer:
The wavelength is calculated by rearranging the formula \( v = f \times \lambda \) to \( \lambda = \frac{v}{f} \).
Given speed \( v = 340 \, \text{m/s} \) and frequency \( f = 170 \, \text{Hz} \),
Substitute the values: \( \lambda = \frac{340}{170} = 2 \, \text{m} \).
The wavelength of the wave is 2 metres.
This means the distance between two peaks of the wave is 2 metres.
Question 7
Explain why sound waves have different speeds in air and water.
Answer:
Sound waves travel by vibrating particles in a medium, and their speed depends on the medium’s properties.
In water, particles are closer together and more tightly packed than in air.
This allows vibrations to transfer faster between particles, so sound travels quicker in water.
In air, particles are more spread out, which slows down the transfer of vibrations.
Therefore, sound speed is higher in water than in air because the particles are closer and transfer energy more easily.
Temperature and density also affect sound wave speed.
Question 8
If the wave speed is 12 m/s and the period is 0.5 seconds, find the frequency and wavelength of the wave.
Answer:
First, find the frequency using \( f = \frac{1}{T} \).
Given \( T = 0.5 \, \text{s} \), so \( f = \frac{1}{0.5} = 2 \, \text{Hz} \).
Next, calculate the wavelength from \( v = f \times \lambda \).
Rearranged, \( \lambda = \frac{v}{f} \).
Substitute \( v = 12 \, \text{m/s} \) and \( f = 2 \, \text{Hz} \):
\( \lambda = \frac{12}{2} = 6 \, \text{m} \).
So, the frequency is 2 Hz and the wavelength is 6 metres.
Question 9
What is the period of a wave if its wavelength is 3 m and the speed is 12 m/s?
Answer:
Use the formula \( v = f \times \lambda \) to find frequency \( f = \frac{v}{\lambda} \).
Given \( v = 12 \, \text{m/s} \) and \( \lambda = 3 \, \text{m} \),
Divide: \( f = \frac{12}{3} = 4 \, \text{Hz} \).
Now calculate the period \( T = \frac{1}{f} \).
So, \( T = \frac{1}{4} = 0.25 \, \text{s} \).
The period of the wave is 0.25 seconds.
Question 10
A wave’s frequency is 15 Hz and its wavelength is 0.8 m. Describe how to calculate the wave speed and then find it.
Answer:
To calculate the wave speed, use the equation \( v = f \times \lambda \).
Frequency means how many waves pass in one second, and wavelength is the length of one wave.
Multiply the frequency by the wavelength to find the speed.
Given frequency \( f = 15 \, \text{Hz} \) and wavelength \( \lambda = 0.8 \, \text{m} \),
Calculate wave speed: \( v = 15 \times 0.8 = 12 \, \text{m/s} \).
Hence, the wave travels at a speed of 12 metres per second.
⚙️ 10 Examination-Style 6-Mark Questions on Wavelength, Frequency, Period, and Wave Speed
Question 1
Explain the relationship between wavelength, frequency, and wave speed. How does changing the frequency of a wave affect its wavelength if the wave speed remains constant?
Answer:
Wavelength is the distance between two consecutive peaks of a wave, frequency is how many waves pass a point per second, and wave speed is the distance the wave travels per second. They are related by the equation: wave speed = frequency × wavelength.
If the wave speed remains the same and the frequency increases, the wavelength must decrease to keep the equation balanced. This means higher frequency waves have shorter wavelengths, and lower frequency waves have longer wavelengths.
For example, sound waves of higher pitch (frequency) have shorter wavelengths if they travel at the same speed. The relationship is inversely proportional between frequency and wavelength when speed is constant.
This concept helps explain why different types of waves, like radio and light waves, look and behave differently. Understanding this is important in physics as it helps us describe wave behaviour accurately.
Question 2
A wave has a frequency of 25 Hz and a wavelength of 4 m. Calculate its wave speed and explain the significance of your answer.
Answer:
The wave speed (v) can be found using the formula v = frequency × wavelength. Substituting the values, v = 25 Hz × 4 m = 100 m/s.
This means the wave moves 100 metres every second.
Wave speed tells us how fast energy or information is transferred by the wave. In real life, this speed could represent how fast sound travels through air or how fast ripples move across water.
Knowing wave speed helps in designing technologies like radios and ultrasound machines. It also helps scientists understand natural phenomena such as earthquakes or light travelling through different mediums.
The calculation shows how frequency and wavelength together determine how quickly waves move. Understanding this is crucial for solving physics problems related to waves.
Question 3
Describe how the period of a wave is related to its frequency. Give an example using a wave with a frequency of 10 Hz.
Answer:
The period of a wave is the time it takes for one complete wave to pass a point, and it is the reciprocal of frequency. This means period (T) = 1 / frequency (f).
For a wave with a frequency of 10 Hz, the period would be T = 1 / 10 = 0.1 seconds.
This means each wave cycle takes 0.1 seconds to pass.
Frequency and period are inversely related: as frequency increases, period decreases.
If a wave vibrates more times per second, the time for each wave to pass is shorter. This relationship helps us understand wave motion and timing.
For example, sound waves with higher frequencies have smaller periods, making the sound higher in pitch. Calculating period from frequency is important in physics to analyse wave properties and their effects.
Question 4
A water wave travels at 2 m/s with a frequency of 0.5 Hz. Calculate the wavelength of the wave and explain the physical meaning of the result.
Answer:
Using the formula wave speed = frequency × wavelength, rearranged to wavelength = wave speed / frequency, we substitute the values: wavelength = 2 m/s ÷ 0.5 Hz = 4 m.
The wavelength of 4 metres means the distance between successive peaks of the water wave is 4 metres.
This distance is how far the wave spreads out in space as it moves through water. A longer wavelength indicates the waves are more spread out.
The frequency of 0.5 Hz means half a wave passes a point every second, so the wave cycles slowly.
Understanding wavelength helps predict wave behaviour on water surfaces, including how energy moves and interacts with obstacles. This knowledge is useful for boats, coastal engineering, and studying natural wave effects.
Question 5
If the frequency of a wave doubles, what happens to its period? Explain what this means physically and how it relates to real-world examples.
Answer:
If the frequency doubles, the period halves because period is the inverse of frequency.
Mathematically, T = 1 / f, so if frequency f becomes 2f, then T becomes 1 / (2f) = T / 2.
Physically, this means waves pass points twice as frequently but each wave cycle takes half the time to complete.
For example, if a sound wave’s frequency doubles, the pitch sounds higher with shorter wave cycles.
This is why musical notes sound different when frequency changes: doubling frequency raises the note by one octave.
In real life, frequency and period changes affect the behaviour of light, sound, and water waves.
This inverse relationship is critical for wave analysis across many physics applications.
Question 6
Explain why light speed is constant in a vacuum but frequency and wavelength can change when light moves between different materials.
Answer:
Light speed is constant in a vacuum because there are no particles to slow it down, and all electromagnetic waves travel at the same maximum speed (about 3 × 10^8 m/s).
However, when light enters different materials like glass or water, it slows down due to interactions with atoms.
The frequency, determined by the light source, stays the same because it is linked to the energy of photons and does not change as light crosses materials.
Since wave speed decreases but frequency remains constant, the wavelength must decrease according to the equation: wave speed = frequency × wavelength.
This change in wavelength explains effects like refraction where light bends passing through different materials.
This concept shows how wave properties adapt depending on the medium.
Question 7
A sound wave in air has a period of 0.002 seconds. Calculate its frequency and explain how this relates to the sounds humans can hear.
Answer:
Frequency is the inverse of period, so frequency = 1 / period = 1 / 0.002 = 500 Hz.
This means 500 waves pass a point every second.
Sounds with a frequency of 500 Hz are in the audible range for humans, which is roughly from 20 Hz to 20,000 Hz.
This frequency corresponds to a mid-range tone, common in everyday sounds like speech or music notes.
Understanding frequency helps explain why different sounds have different pitches: higher frequency waves make higher pitches.
Knowing wave frequency also helps in fields such as audio engineering and hearing science.
Calculating frequency from period is an important skill in wave physics and practical sound applications.
Question 8
Describe what happens to the wavelength of a wave if its speed halves but its frequency stays the same. Use the wave equation in your explanation.
Answer:
The wave equation states wave speed = frequency × wavelength.
If the wave speed halves but frequency stays constant, wavelength must also halve to keep the equation true.
This is because wavelength = wave speed / frequency.
For example, if originally wave speed was 10 m/s and wavelength was 5 m with frequency 2 Hz, halving speed to 5 m/s keeps frequency at 2 Hz, so wavelength becomes 5 m/s ÷ 2 Hz = 2.5 m.
Physically, this means waves become “shorter” in space because the distance between wave peaks decreases.
This effect is important when waves travel through different materials, influencing how waves appear and behave.
Changes in wavelength affect wave properties like energy distribution and interference patterns.
Question 9
A wave pulse takes 0.05 seconds to travel 25 metres. Calculate the wave speed and then determine its frequency if the wavelength is 5 metres.
Answer:
Wave speed is distance divided by time: speed = 25 m ÷ 0.05 s = 500 m/s.
Given wavelength = 5 m, frequency can be calculated using frequency = wave speed / wavelength = 500 m/s ÷ 5 m = 100 Hz.
This means 100 waves pass a point per second.
Knowing speed and frequency helps describe how fast energy moves and how many wave cycles occur in a given time.
The wave could be a sound wave travelling at high speed or other mechanical wave types.
Such calculations are important for understanding wave motion in physics and apply to everyday technologies like telecommunications and medical imaging.
Question 10
Explain why period and wavelength are used together to describe waves and how each contributes to understanding wave behaviour in physics.
Answer:
Period and wavelength are both essential because they describe different aspects of wave behaviour: period measures the time for one wave cycle, while wavelength measures the distance of one wave cycle.
Together with frequency and wave speed, they provide a full description of the wave’s characteristics.
Period and wavelength help us understand how frequently waves occur in time and how spread out they are in space.
For example, sound waves’ pitch depends on frequency (and thus period), while the wavelength impacts how the wave interacts with environments, like reflection or diffraction.
In physics, combining period and wavelength allows predicting how waves transfer energy, how they interfere, and how they behave in different media.
They form a foundation for more complex wave phenomena analysis.
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These 10 exam-style questions cover wavelength, frequency, period, and wave speed for Year 10 Physics, with detailed answers to help students understand key concepts clearly.
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