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What is the Frequency of a Trigonometric Wave?
Grade Level:
Class 10
AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine
Definition
What is it?
The frequency of a trigonometric wave tells us how many complete cycles or repetitions the wave makes in one second. It's like counting how many times a swing goes back and forth in a given time. A higher frequency means the wave repeats more quickly.
Simple Example
Quick Example
Imagine your favourite song playing on the radio. If the sound wave has a high frequency, the music will sound like a high-pitched whistle. If it has a low frequency, it will sound like a deep hum. This is why different musical notes have different frequencies.
Worked Example
Step-by-Step
Let's find the frequency of a wave that completes 10 cycles in 2 seconds.
Step 1: Understand what 'frequency' means. Frequency is cycles per second.
---Step 2: Identify the total number of cycles given. Here, it's 10 cycles.
---Step 3: Identify the total time taken for these cycles. Here, it's 2 seconds.
---Step 4: Use the formula: Frequency = (Number of Cycles) / (Time taken).
---Step 5: Substitute the values: Frequency = 10 cycles / 2 seconds.
---Step 6: Calculate the result: Frequency = 5 cycles/second.
---Step 7: The unit for frequency is Hertz (Hz). So, the frequency is 5 Hz.
Answer: The frequency of the wave is 5 Hz.
Why It Matters
Understanding frequency is crucial in fields like AI/ML for processing audio signals, in Physics for studying light and sound, and in Engineering for designing communication systems. It helps engineers build everything from your mobile phone's network to ISRO's satellite communication, opening doors to careers in technology and research.
Common Mistakes
MISTAKE: Confusing frequency with time period. | CORRECTION: Frequency is how many cycles per second (Hz), while time period is how many seconds per cycle (seconds). They are reciprocals of each other (Frequency = 1 / Time Period).
MISTAKE: Forgetting the units or using the wrong units. | CORRECTION: Frequency is always measured in Hertz (Hz), which means 'cycles per second'. Always write Hz after your numerical answer.
MISTAKE: Calculating frequency when the time given is not in seconds. | CORRECTION: Always convert the given time into seconds before calculating frequency. For example, if time is in minutes, multiply by 60 to get seconds.
Practice Questions
Try It Yourself
QUESTION: A fan completes 30 rotations in 5 seconds. What is its frequency in Hz? | ANSWER: 6 Hz
QUESTION: A radio wave completes 1200 cycles in 1 minute. What is its frequency in Hz? | ANSWER: 20 Hz
QUESTION: If a wave has a time period of 0.25 seconds, what is its frequency? (Hint: Frequency = 1 / Time Period) | ANSWER: 4 Hz
MCQ
Quick Quiz
What does a higher frequency of a sound wave indicate?
The sound is louder
The sound has a lower pitch
The sound has a higher pitch
The sound travels slower
The Correct Answer Is:
C
A higher frequency means the wave repeats more often, which corresponds to a higher pitch in sound. Options A, B, and D are incorrect as loudness relates to amplitude, lower pitch to lower frequency, and speed of sound is generally constant in a medium.
Real World Connection
In the Real World
In India, FM radio stations like 'Radio Mirchi 98.3 FM' use frequency to identify their channels. The '98.3' refers to 98.3 Megahertz (MHz), which is the frequency at which the radio waves are transmitted. Your radio receiver tunes into this specific frequency to catch your favourite RJ and music.
Key Vocabulary
Key Terms
FREQUENCY: Number of cycles per second, measured in Hertz (Hz) | CYCLE: One complete oscillation or repetition of a wave | TIME PERIOD: Time taken for one complete cycle of a wave (seconds) | HERTZ (Hz): The unit of frequency, meaning one cycle per second | WAVE: A disturbance that transfers energy without transferring matter
What's Next
What to Learn Next
Now that you understand frequency, you can explore 'Time Period of a Wave'. It's closely related to frequency and will help you describe waves even better. Keep up the great work!
