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Detailed Explanation of Wavelength, Frequency, Period, and Wave Speed ⚡🌊
Wavelength (λ) 📏
Definition: Wavelength is the distance between two successive points that are in phase on a wave. This means it is the length of one complete wave cycle, such as the distance from one crest to the next crest or from one trough to the next trough.
Units: The SI unit for wavelength is the metre (m).
Key idea: Wavelength tells us how long one wave is in space.
Frequency (f) 🎵
Definition: Frequency is the number of complete waves that pass a fixed point every second.
Units: The unit of frequency is the hertz (Hz), where 1 Hz means one wave per second.
Key idea: Frequency tells us how often waves happen in time.
Period (T) ⏳
Definition: The period is the time taken for one complete wave to pass a point, which is the reciprocal of frequency.
Units: The unit for the period is the second (s).
Relation to frequency:
T = 1 / f
This means if the frequency is high, the period is short and vice versa.
Wave Speed (v) 🏃♂️💨
Definition: Wave speed is how fast a wave travels through a medium.
Units: The unit is metres per second (m/s).
Important formula:
v = f × λ
This means the speed of a wave is equal to the frequency multiplied by the wavelength.
How They Relate Together 🔄
- If you know the frequency of a wave and its wavelength, you can calculate how fast the wave is moving using the formula above.
- Since the period is how long one wave takes to pass, and frequency is how many waves pass per second, their relationship is crucial in understanding wave timing.
- The wavelength gives the size of the wave, while frequency tells you how many waves happen in one second. Multiplying these gives the wave speed, which connects space and time properties of the wave.
Practical Study Tip ✍️
When studying waves, write out all the symbols and units clearly. For example:
| Quantity | Symbol | Unit | Meaning |
|---|---|---|---|
| Wavelength | λ | metres (m) | Distance between wave peaks |
| Frequency | f | hertz (Hz) | Waves per second |
| Period | T | seconds (s) | Time for one wave to pass |
| Wave speed | v | m/s | Distance travelled by wave per second |
Using diagrams of waves helps, too. Label the wavelength, point out one period on a time graph, and visualise frequency as the number of waves passing per second.
By mastering these basic terms — wavelength, frequency, period, and wave speed — you’ll be well prepared to tackle wave questions in exams confidently!
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 - The number of waves passing a point per second is called what?
Answer: Frequency - What is the term for the time taken for one complete wave to pass a point?
Answer: Period - What is the physical quantity symbolised by the letter
vin wave calculations?
Answer: Speed - Frequency is the reciprocal of which other wave property?
Answer: Period - If a wave has a high frequency, does it have a longer or shorter wavelength?
Answer: Shorter - What unit is frequency measured in?
Answer: Hertz - What unit is period measured in?
Answer: Seconds - Wave speed equals wavelength multiplied by what?
Answer: Frequency - What part of the wave is located between a crest and a trough?
Answer: Amplitude
10 Examination-Style 2-Mark Questions on Wavelength, Frequency, Period, and Wave Speed 📚
- Define the wavelength of a wave.
Wavelength is the distance between two consecutive points in phase on a wave, such as crest to crest. - What is the unit of frequency in the International System of Units (SI)?
The unit of frequency is hertz (Hz). - How is the period of a wave related to its frequency?
The period is the reciprocal of the frequency, so period = 1/frequency. - Calculate the frequency of a wave with a period of 0.02 seconds.
Frequency = 1 / 0.02 s = 50 Hz. - A wave has a speed of 340 m/s and a frequency of 170 Hz. What is its wavelength?
Wavelength = speed / frequency = 340 m/s ÷ 170 Hz = 2 m. - Describe what happens to the wave speed if the frequency increases but wavelength stays the same.
Wave speed increases because speed = frequency × wavelength. - If a wave has a wavelength of 0.5 m and a speed of 10 m/s, what is its frequency?
Frequency = speed / wavelength = 10 m/s ÷ 0.5 m = 20 Hz. - Explain the physical meaning of the period of a wave.
The period is the time taken for one complete wave cycle to pass a point. - Calculate the wave speed of a wave with a frequency of 25 Hz and a wavelength of 0.4 m.
Wave speed = frequency × wavelength = 25 Hz × 0.4 m = 10 m/s. - Why can the period and frequency never be zero for a travelling wave?
Because a wave must have continuous oscillations, so it must have a finite period and frequency.
10 Examination-Style 4-Mark Questions on Wavelength, Frequency, Period, and Wave Speed 📝
Question 1
A water wave has a wavelength of 2 metres and travels at a speed of 4 m/s. Calculate the frequency of the wave.
Answer:
To find the frequency, use the formula f = v / λ, where v is the wave speed and λ is the wavelength. Substituting, f = 4 m/s ÷ 2 m = 2 Hz. This means the wave has 2 complete cycles per second. Frequency is measured in hertz (Hz), which shows how many waves pass a point in one second. Understanding frequency helps us describe how fast a wave oscillates. This is important in many areas, like sound and light.
Question 2
Explain the relationship between frequency and period in a wave.
Answer:
Frequency and period are related because they describe wave oscillations but in different ways. Frequency is the number of waves per second, measured in hertz (Hz), while period is the time taken for one complete wave cycle, measured in seconds (s). They are inversely related, which means f = 1/T and T = 1/f. If frequency increases, the period decreases because waves happen faster. If frequency decreases, the period gets longer. This relationship helps us understand the timing of wave motions.
Question 3
A wave has a frequency of 5 Hz and a period of 0.2 seconds. Verify if these values are correct and explain your reasoning.
Answer:
Using the formula T = 1/f, if f = 5 Hz, then T = 1/5 = 0.2 s. This matches the given period, so the values are consistent. Frequency and period must always be inversely related. If the period was different, that would mean the frequency was incorrect. Checking these values is important in physics problems to ensure calculations are accurate. It shows the importance of understanding the relationship between time and wave cycles.
Question 4
Calculate the wave speed of a sound wave if the wavelength is 0.7 m and the frequency is 500 Hz.
Answer:
Wave speed can be calculated using v = f × λ. Substituting the values gives v = 500 × 0.7 = 350 m/s. This is the speed at which the sound waves travel through the air. The wave speed depends on the medium but here, it matches typical values for sound in air. Knowing how to find wave speed is crucial for understanding how waves move and how we hear sounds. It also applies to other waves like light and water waves.
Question 5
Describe how changing the frequency affects the wavelength of a wave if its speed remains constant.
Answer:
If wave speed is constant, an increase in frequency causes the wavelength to decrease. This is because v = f × λ, and if v stays the same, then λ = v / f. When frequency goes up, wavelength must go down to keep the equation balanced. Conversely, if frequency decreases, the wavelength increases. This inverse relationship helps explain phenomena like light colour changes or pitch changes in sound. It helps us understand wave behaviour in different contexts.
Question 6
A light wave has a period of 4 × 10-15 seconds. Calculate the frequency of this light wave.
Answer:
Frequency is calculated using f = 1 / T. So, f = 1 / (4 × 10-15) = 2.5 × 1014 Hz. This is a very high frequency, typical of visible light waves. Such electromagnetic waves oscillate extremely fast compared to waves like sound. Knowing this helps when studying different types of waves in physics. It also explains why light has such energy and speed properties.
Question 7
An ocean wave travels at 10 m/s and its frequency is 0.5 Hz. What is the wavelength of the ocean wave?
Answer:
Using λ = v / f, substitute given values: λ = 10 / 0.5 = 20 m. The wavelength is therefore 20 metres. Wavelength tells us the distance between wave crests. For ocean waves, this affects how the wave looks and behaves near the shore. Understanding wavelength helps in safety and in predicting wave effects.
Question 8
Explain why the period of a wave gives information about the time between successive crests passing a point.
Answer:
The period T is defined as the time for one complete wave cycle to pass a fixed point. Since each cycle includes one wave crest, the period directly indicates the time interval between two crests arriving at that point. For example, if the period is 1 second, a crest passes every second. This is essential for timing wave-related events like tides or sound waves. The regularity of periods helps with predicting wave patterns. It is an important concept in understanding wave motion.
Question 9
A student measures the wave speed of a wave as 3 m/s and frequency as 3 Hz. Calculate the period and wavelength of the wave.
Answer:
First find the period: T = 1 / f = 1 / 3 = 0.33 s. Next, find the wavelength: λ = v / f = 3 / 3 = 1 m. The period is the time for one wave cycle, and the wavelength is the distance between crests. Both values help describe the wave fully. This shows understanding of all four key properties: speed, frequency, wavelength, and period.
Question 10
Why is it important to remember the units when calculating wave speed, frequency, period, and wavelength?
Answer:
Using correct units is vital because formulas rely on consistent measurements. Wave speed is usually in metres per second (m/s), frequency in hertz (Hz), period in seconds (s), and wavelength in metres (m). Mixing units, like cm and m/s, will give wrong answers. Units help identify what quantities mean in the real world, like how far or fast waves move. Always check units before calculating to avoid mistakes. This habit improves accuracy in physics and science exams.
10 Examination-Style 6-Mark Questions on Wavelength, Frequency, Period, and Wave Speed 🔍
Question 1
Explain the relationship between wavelength, frequency, and wave speed. Use the formula relating these quantities and describe what each term represents.
Answer:
The wave speed (v) is equal to the product of wavelength (λ) and frequency (f), given by the equation v = f × λ. Wavelength is the distance between two successive points in phase on a wave, such as crest to crest. Frequency is how many waves pass a given point per second, measured in hertz (Hz). Wave speed is how fast the wave travels through the medium, measured in metres per second (m/s). This formula shows that if the frequency increases and wavelength stays the same, the wave speed increases. Alternatively, if the wavelength increases but frequency decreases proportionally, the wave speed may remain constant. This relationship is crucial because it links observable properties of a wave to how fast it moves. For example, light waves in air travel at a constant speed, so if the frequency changes, the wavelength adjusts to keep the speed fixed. Understanding this helps in solving problems involving waves in different media.
Question 2
A wave has a frequency of 500 Hz and a wavelength of 0.6 m. Calculate its wave speed and explain each step clearly.
Answer:
To find the wave speed, use the formula v = f × λ. First, identify the frequency (f) which is 500 Hz, meaning 500 waves pass a point each second. The wavelength (λ) is 0.6 m, the distance between two crests. Multiply frequency by wavelength: 500 × 0.6 = 300. This gives a wave speed (v) of 300 m/s. This means the wave moves 300 metres every second through its medium. Understanding each value helps show how quickly and how often the wave oscillates. This calculation is important in fields like acoustics and light where knowing wave speed determines how waves transfer energy. Always check that units are correct (Hz for frequency, metres for wavelength) before calculating.
Question 3
Describe how the period of a wave is related to its frequency and provide an example to support your explanation.
Answer:
The period (T) of a wave is the time taken for one complete wave cycle to pass a given point. Frequency (f) is the number of waves passing per second. They are inversely related, expressed by T = 1/f. If frequency increases, meaning more waves pass each second, the period decreases because each wave takes less time. For example, a wave with frequency 10 Hz has a period of 1/10 = 0.1 seconds, meaning each wave cycle lasts 0.1 seconds. This inverse relationship is key because it links time-based wave properties. When studying sound, a high-frequency wave results in a high-pitched sound with a short period. Understanding period and frequency helps explain wave behaviour in physics exams and practical experiments.
Question 4
Explain how wave speed changes when a wave moves from air into water and the effect on its frequency, wavelength, and period.
Answer:
When a wave moves from air into water, its wave speed changes because water is denser than air, usually slowing down mechanical waves like sound. The frequency remains constant since it depends on the source of the wave, not the medium. However, because speed changes and frequency is constant, the wavelength must adjust according to v = f × λ. Since speed decreases in water, wavelength becomes shorter. The period, which is the reciprocal of frequency, stays the same because frequency is unchanged. This means each wave takes the same amount of time to complete one cycle, even though it moves slower and with a smaller wavelength. Understanding these concepts is important when studying wave behaviour through different materials, a common topic in Year 11 Physics.
Question 5
A student measures a wave with a period of 0.02 seconds. Calculate the frequency of the wave and explain how these two quantities relate.
Answer:
The relationship between period (T) and frequency (f) is f = 1/T. Given the period T = 0.02 seconds, the frequency is f = 1 / 0.02 = 50 Hz. This means 50 waves pass any fixed point every second. The period is the time taken for one complete wave cycle to pass, while frequency is how many cycles occur in one second. These two quantities are inversely proportional: when one increases, the other decreases. In this example, a short period results in a high frequency. This relationship helps us understand wave motion, particularly in sound waves where frequency determines pitch. Remembering f = 1/T is very useful for solving various wave problems in physics.
Question 6
Describe what happens to the wavelength and frequency of a wave if its wave speed doubles while the frequency stays the same.
Answer:
If the wave speed doubles but the frequency remains the same, the wavelength must also double. This can be explained using the formula v = f × λ. Since frequency (f) is constant, any change in wave speed (v) must be matched by the same proportional change in wavelength (λ). So, a doubling in wave speed results in the wavelength increasing by a factor of two. The frequency does not change because it depends on the source of the wave, not the medium or wave speed. This means waves become longer but still have the same number of oscillations per second. This concept is vital in physics for understanding how waves behave when moving between different materials or under different conditions.
Question 7
A sound wave travels through air with a speed of 340 m/s and frequency of 680 Hz. Calculate the wavelength and describe how these values relate to what we hear.
Answer:
Using v = f × λ, rearranged to λ = v / f, the wavelength λ = 340 m/s ÷ 680 Hz = 0.5 metres. The wavelength here is half a metre, indicating the distance between successive compressions in the air. Frequency at 680 Hz corresponds to the number of sound waves per second, which determines the pitch of the sound. A higher frequency corresponds to a higher pitch. The wave speed indicates how fast sound travels through the air. These factors combined determine what we hear: the pitch is decided by frequency, and knowing the wavelength helps understand how sound interacts with different environments. This makes it easier for students to connect physics with everyday experiences of hearing.
Question 8
Explain why the period of a wave does not change when it moves from one medium to another.
Answer:
The period of a wave is determined by the source of the wave and how often it creates oscillations, not by the medium through which it travels. Therefore, when a wave moves from one medium to another, the period remains constant. This is because period is the reciprocal of frequency (T = 1/f), and frequency depends only on the source frequency. Although the wave speed and wavelength change when the wave enters a different medium, the frequency—and by extension, the period—do not change. This principle is essential for understanding wave behaviour at boundaries, which is a common topic in physics exams. It also helps explain why a musical note’s pitch stays the same whether sound travels through air or water.
Question 9
A wave has a wavelength of 2 m and a period of 4 seconds. Calculate its frequency and wave speed.
Answer:
First, calculate frequency using f = 1/T. Given period T = 4 s, frequency f = 1 / 4 = 0.25 Hz. This means one wave passes every 4 seconds. Using v = f × λ, wave speed v = 0.25 Hz × 2 m = 0.5 m/s. So, the wave moves at 0.5 metres per second. These calculations link the time-based concept of period to frequency and spatial properties like wavelength and wave speed. Understanding how to calculate these values is crucial for analysing wave problems. This example shows that longer period means low frequency and slower wave speed if wavelength remains fixed.
Question 10
Discuss how understanding wave speed, frequency, period, and wavelength helps in practical physics problems, giving an example.
Answer:
Understanding wave speed, frequency, period, and wavelength is essential for solving problems related to sound, light, and water waves. These concepts help predict how waves behave and transfer energy. For example, in a physics experiment measuring sound waves, knowing the frequency allows calculation of wavelength if wave speed is known, or vice versa, using v = f × λ. This helps identify the type of wave or medium properties. In real life, engineers use these principles to design better speakers by adjusting frequencies for clearer sound or calculate safe distances for radio wave transmissions. Being able to switch between period and frequency also helps calculate time intervals in waves. Practising these helps improve exam performance and builds a strong foundation for more advanced physics topics.
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