A student claims that if a sound wave has a time period of 0.01 s, its frequency must be lower than that of a wave with a time period of 0.005 s. Is this statement correct based on the relation between frequency and time period?
Yes, because frequency decreases as time period increases
Frequency and time period are reciprocals of each other: \(f = \frac{1}{T}\). So a larger time period means a smaller frequency, and vice versa.
For \(T = 0.01\text{ s}\): \(f = \frac{1}{0.01} = 100\text{ Hz}\). For \(T = 0.005\text{ s}\): \(f = \frac{1}{0.005} = 200\text{ Hz}\).
Since 100 Hz is lower than 200 Hz, the wave with the longer time period (0.01 s) has the lower frequency, so the student's claim is correct.
Check: \(f \times T = 100 \times 0.01 = 1\) and \(200 \times 0.005 = 1\), confirming both values satisfy \(fT = 1\); frequency is neither unrelated to time period nor constant, and it does not increase with time period.
Hence, Yes, because frequency decreases as time period increases.
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