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? a) wave b has the higher frequency. its frequency is 7 hz. b) wave a has the higher frequency.

Explanation:

Step1: Recall frequency formula

Frequency \( f \) is the reciprocal of period \( T \), so \( f=\frac{1}{T} \).

Step2: Calculate frequency of Wave A

Period of Wave A, \( T_A = \frac{4}{100}\) s. Then \( f_A=\frac{1}{T_A}=\frac{1}{\frac{4}{100}}=\frac{100}{4} = 25 \) Hz.

Step3: Calculate frequency of Wave B

Period of Wave B, \( T_B=\frac{1}{7}\) s. Then \( f_B=\frac{1}{T_B}=\frac{1}{\frac{1}{7}} = 7 \) Hz.

Step4: Compare frequencies

Since \( 25>7 \), Wave A has higher frequency. But wait, let's check the options again. Wait, maybe I misread the period of Wave A? Wait, the problem says Wave A has period \( \frac{4}{100} \) second (which is 0.04 s) and Wave B has \( \frac{1}{7} \) s (≈0.1429 s). So frequency of A: \( 1/0.04 = 25 \) Hz, frequency of B: \( 1/(1/7)=7 \) Hz. So Wave A has higher frequency. But let's check the options. Option B says "Wave A has the higher frequency" (even though the text is cut, but from calculation, A's frequency is 25 Hz, B's is 7 Hz. So Wave A has higher frequency. Wait, but let's re - check the calculation.

Wait, maybe the original problem's Wave A period is \( \frac{4}{100} \) (0.04) and Wave B is \( \frac{1}{7} \) (≈0.142857). So \( f_A = 1/0.04=25 \) Hz, \( f_B = 7 \) Hz. So Wave A has higher frequency. So the correct option should be B (assuming option B is "Wave A has the higher frequency..."). Wait, but let's check the options again. Option A says Wave B has higher frequency (7 Hz), but our calculation shows Wave A has 25 Hz which is higher. So the correct option is B. Wait, maybe I made a mistake? Wait, period is time for one cycle, so higher frequency means more cycles per second, so smaller period. Wave A has smaller period (0.04 s) than Wave B (≈0.1429 s), so Wave A has higher frequency. So the correct option is B.

Answer:

B) Wave A has the higher frequency. (Assuming the full option B states that Wave A has higher frequency, as per the calculation where \( f_A = 25 \) Hz and \( f_B = 7 \) Hz, so Wave A has higher frequency.)