Question

listen
your boss asks you compare two sound waves and determine which has the higher frequency. wave a has a period of $\frac{4}{100}$ second and wave b has a period of $\frac{1}{7}$ second. what would you tell your boss?
a) wave a has the higher frequency. its frequency is 4 hz.
b) wave a has the higher frequency. its frequency is 25 hz.
c) wave b has the higher frequency. its frequency is 42 hz.
d) wave b has the higher frequency. its frequency is 7 hz.

Explanation:

Step1: Recall frequency-period relation

Frequency $f = \frac{1}{T}$, where $T$ is period.

Step2: Calculate Wave A's frequency

$T_A = \frac{4}{100}\ \text{s}$, so $f_A = \frac{1}{\frac{4}{100}} = \frac{100}{4} = 25\ \text{Hz}$

Step3: Calculate Wave B's frequency

$T_B = \frac{1}{7}\ \text{s}$, so $f_B = \frac{1}{\frac{1}{7}} = 7\ \text{Hz}$

Step4: Compare the two frequencies

$25\ \text{Hz} > 7\ \text{Hz}$, so Wave A has higher frequency.

Answer:

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