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Wave A has a period of 4⁄100 second and Wave B has a period of 1⁄7 second. Which wave has the higher frequency?

Question 17 options:

A)

Wave B has the higher frequency. Its frequency is 7 Hz.

B)

Wave A has the higher frequency. Its frequency is 25 Hz.

C)

Wave A has the higher frequency. Its frequency is 4 Hz.

D)

Wave B has the higher frequency. Its frequency is 42 Hz.

1 answer

To find which wave has a higher frequency, we can use the formula for frequency, which is the inverse of the period:

\[ \text{Frequency} (f) = \frac{1}{\text{Period} (T)} \]

  1. Calculating the frequency of Wave A:

    • The period of Wave A is \( \frac{4}{100} \) seconds (which is 0.04 seconds).
    • Therefore, the frequency of Wave A is: \[ f_A = \frac{1}{T_A} = \frac{1}{0.04} = 25 \text{ Hz} \]

  2. Calculating the frequency of Wave B:

    • The period of Wave B is \( \frac{1}{7} \) seconds.
    • Therefore, the frequency of Wave B is: \[ f_B = \frac{1}{T_B} = \frac{1}{\frac{1}{7}} = 7 \text{ Hz} \]

Now that we have the frequencies:

  • Wave A: 25 Hz
  • Wave B: 7 Hz

Conclusion: Wave A has the higher frequency.

The correct answer is B) Wave A has the higher frequency. Its frequency is 25 Hz.