Question

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.

Answer 1

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.**